We present a new method for assessing the strength of fuzzy rules with respect to a dataset, based on the measures of the greatest energy and smallest entropy of a fuzzy relation. Considering a fuzzy automaton (relation) in which A is the input fuzzy set and B the output fuzzy set, the fuzzy relation R1 with greatest energy provides information about the greatest strength of the input-output and the fuzzy relation R2 with the smallest entropy provides information about uncertainty of the relationship input-output. We consider a new index of the fuzziness of the input-output based over R1 and R2. In our method this index is calculated for each pair of input and output fuzzy sets in a fuzzy rule. A threshold value is set for choosing the most relevant fuzzy rules with respect to the data.

We define a new seasonal forecasting method based on fuzzy transforms. We use the best interpolating polynomial for extracting the trend of the time series and generate the inverse fuzzy transform on each seasonal subset of the universe of discourse for predicting the value of a an assigned output. Like first example, we use the daily weather dataset of the municipality of Naples (Italy) starting from data collected from 2003 till to 2015 making predictions on the following outputs: mean temperature, max temperature and min temperature, all considered daily. Like second example, we use the daily mean temperature measured at the weather station “Chiavari Caperana” in the Liguria Italian Region. We compare the results with our method, the average seasonal variation, ARIMA and the usual fuzzy transforms concluding that the best results are obtained under our approach in both examples.

In this paper, we introduce the application of Type-I fuzzy inference systems (FIS) as an alternative to improve the prioritization in the FMECA analysis applied in cyber-power grids. Classical FMECA assesses the risk level through the Risk Priority Number (RPN). The multiplication between three integer numbers computes this, called risk factors, representing the severity, occurrence, and detectability of each failure mode and are defined by a team of experts. The RPN does not consider any relative importance between the risk factors and may not necessarily represent the real risk perception of the FMECA team members, usually expressed by natural language; this is the main FMECA shortcoming criticized in the literature. Our approach considers fuzzy variables defined by FMECA experts to represent the uncertainty associated with the human language and a rule base consisting of 125 fuzzy rules to represent the risk perception of the experts. To test our approach, we select a cyber-power grid previously analyzed by the authors using the classical FMECA. The results reveal our proposed fuzzy approach as promissory to represent the uncertainty associated with expert knowledge and to perform an accurate prioritization of failure modes in the context of electrical power systems.

This paper focuses on evaluating airline service quality from the perspective of passengers view. Until now a lot of researches has performed in airline service quality evaluation in the world but a little research has been conducted in Iran, yet. In this research a framework for measuring airline service quality in Iran is proposed. After reviewing airline service quality criteria, SSQAI model was selected because of its comprehensiveness in covering airline service quality dimensions. SSQAI questionnaire items were redesigned to adopt with Iranian airlines requirements and environmental circumstances in the Iran's economic and cultural context. This study includes fuzzy decision-making theory, considering the possible fuzzy subjective judgment of the evaluators during airline service quality evaluation. Fuzzy TOPSIS have been applied for ranking airlines service quality performances. Three major Iranian airlines which have the most passenger transfer volumes in domestic and foreign flights, were chosen for evaluation in this research. Results demonstrated Mahan airline has got the best service quality performance rank in gaining passengers' satisfaction with delivery of high quality services to its passengers, among the three major Iranian airlines. IranAir and Aseman airlines placed in the second and third rank, respectively, according to passenger's evaluation.Statistical analysis have been used in analyzing passenger responses. Due to abnormality of data, Non-parametric tests were applied. To demonstrate airline ranks in every criterion separately, Friedman test was performed. Variance analysis and Tukey test were applied to study the influence of increasing in age and educational level of passengers' on degree of their satisfaction from airline's service quality. Results showed that age has not significant relation with passenger satisfaction of airlines, however increasing in educational level demonstrated a negative impact on passengers' satisfaction from airline's service quality.

In this paper, it is introduced the notion of r-fuzzy β-T_i, i = 0, 1, 2 separation axioms related to a fuzzy operator β on the initial set X which is a generalization of previous fuzzy separation axioms. An r-fuzzy α-connectedness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of r-fuzzy connectedness. An r-fuzzy α-compactness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of fuzzy compactness.

The article explores Qualitative Comparative Analysis (QCA), an approach for establishing causal relationships between conditions and outcomes. QCA, applied in case studies and empirical analyses, facilitates generalizations for future research and addresses causal complexity by identifying various causal "recipes" leading to the same outcome. Three widely used QCA variants are Crisp-Set QCA (csQCA), Multi-value QCA (mvQCA), and Fuzzy-Set QCA (fsQCA), each with unique approaches. The article emphasizes the significance of bibliometric analysis in mapping a research field's intellectual structure, revealing key contributions and trends. In QCA, bibliometric analysis identifies leading researchers, affiliations, and influential countries. Results show QCA's widespread adoption across disciplines, with continuous growth in article production since 2013. The favored variant is fsQCA, followed by csQCA, and China notably contributes to QCA-related research. In conclusion, QCA proves a potent tool for discerning complex causal relationships in empirical studies, with its increasing interdisciplinary use indicating substantial potential for advancing scientific knowledge.

The aim of this paper is to determine a suitable definition for the concept of fuzzy Hilbert space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Then we considered another approach to the notion of fuzzy inner product and analysed its properties.

The capability of the complex fuzzy sets plays a valuable role to resolve many real life problems. In this paper, we present the compositions of complex fuzzy relations by using the idea of implication operators and max-product compositions of complex fuzzy relations and illustrate these compositions with concrete examples. The converse of these newly invented triangular compositions in terms of compositions of the converse relations are also defined. We also study the interactions with union and intersection. The main goal of this article to present a new technique to enhance medical diagnostic model that can assist to increase the features of healthcare systems. We utilize these compositions to determine the diseases of patients on the basis of intensity of symptoms.

Air pollution is a situation that negatively affects the health of humans and all living things in nature and causes financial damage to the environment. In the case of air pollution, harmful and foreign substances in the air reach an amount and density above normal values. Air pollution also causes climate change, which affects global warming. Particulate matter is a harmful substance that harms the health of humans and other living things, causes air pollution, increases radiation, and negatively affects cloud formation. Particulate matter is extremely small solid particles and liquid droplets suspended in the air. PM10, which is less than 10 microns in diameter, is defined as small particles that can remain in the air for a long time and settle in the respiratory tract, damaging the lungs. Many criteria affect PM10 density and changes in density. The main criteria are vehicle traffic and fuel consumption, industrialization, coal, fuel oil and wood-burning heaters, greenhouse gas impact, and unregulated urbanization. It is important to identify the underlying causes of air pollution caused by PM10. In this context, these criteria need to be evaluated to minimize the negative effects of PM10. In the study, monthly average PM10 data between 2019 and 2023 obtained from the Air Monitoring Station in Kocaeli, Türkiye are used. After determining the criteria affecting PM10, the criteria are prioritized with the Intuitionistic Fuzzy AHP (IF-AHP) method by taking expert decision-maker opinions. The proposed decision-making model aims to guide obtaining the important causes of PM10 emission in terms of danger and focusing on these causes. Additionally, PM10 data is analyzed in the context of Covid-19 and a statistical analysis is made. One-way ANOVA is used to evaluate whether there is a significant difference in the average monthly data over the years. Games-Howell test, one of the post-hoc tests, is used for differences between groups (years). The study is important in that it provides a focus on the criteria affecting PM10 with an intuitive fuzzy perspective, along with statistical analysis.

Many authors proposed analytical methods for solving fully fuzzy Sylvester matrix equation (FFSME) based on Vec-operator and Kronecker product. However, these methods are restricted to nonnegative fuzzy numbers and cannot be extended to FFSME with near-zero fuzzy numbers. The main intention of this paper is to develop a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers that provides a wider scope of trapezoidal fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications. This numerical method can solve the trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients and find all possible finite arbitrary solutions for the system. In order to obtain all possible fuzzy solutions, the TrFFSME is transferred to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication between trapezoidal fuzzy numbers. The fuzzy solutions to the TrFFSME are obtained by developing a new two-stage algorithm. To illustrate the proposed method numerical example is solved.

Most of existing fuzzy forecasting models partition historical training time series into fuzzy time series and build fuzzy-trend logical relationship groups to generate forecasting rules. The determination process of intervals is complex and uncertainty. In this paper, we present a novel fuzzy forecasting model based on high-order fuzzy-fluctuation trends and the fuzzy-fluctuation logical relationships of the training time series. Firstly, we compare each data with the data of its previous day in historical training time series to generate a new fluctuation trend time series(FTTS). Then, fuzzify the FTTS into fuzzy-fluctuation time series(FFTS) according to the up, equal or down range and orientation of the fluctuations. Since the relationship between historical FFTS and the fluctuation trend of future is nonlinear, Particle Swarm Optimization (PSO) algorithm is employed to estimate the required parameters. Finally, use the acquired parameters to forecast the future fluctuations. In order to compare the performance of the proposed model with that of the other models, we apply the proposed method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) time series datasets. The experimental results and the comparison results show that the proposed method can be successfully applied in stock market forecasting or such kinds of time series. We also apply the proposed method to forecast Shanghai Stock Exchange Composite Index (SHSECI) to verify its effectiveness and universality.

A hybrid fuzzy MADM method is proposed in this paper for evaluating airline service quality. Fuzzy set theory is used since it helps in measuring the ambiguity of concepts associated with human being’s subjective judgment. After reviewing service quality evaluation models especially in airline industry, SSQAI model was adopted as a construct for evaluating airline service quality in Iran. Fuzzy DEMATEL was applied to determine the degree of influence and impact of criteria on each other and extract cause and effect relations between them that helped in ranking criteria based on degree of relationship. Then, ANP network map was constructed based on the relation map generated from Fuzzy DEMATEL analysis. Fuzzy ANP approach assisted in prioritizing criteria based on the need for improvement and enabled in a more accurate measurement in decision making process taking the advantage of using linguistic variables. Fuzzy DEMATEL results demonstrates that expertise, Problem-solving, and conduct has the most influence on other factors and in opposite Valence, Waiting Time, Comfort are the factors which get the most impact from other factors and according to Fuzzy ANP analysis Valence, Convenience, Problem-solving, and Safety&Security are the factors with most priorities that need improvement.

The aim of this 9th expository article is to conclude a study on domination in two fuzzy models, including t−norm fuzzy graphs and fuzzy graphs. All parts are twofold even if we don’t men- tion, directly. I.e., all results depicts some properties about fuzzy graph and t−norm fuzzy graph.

We generalize the concept of a fuzzy metric by introducing its approximating counterpart in order to make it more appropriate for the study of some problems related to words combinatorics. We establish close relations between fuzzy approximating metrics in case of special $t$-norms and approximating parametrized metrics, discuss some relations between fuzzy approximating metrics and fuzzy partial metrics as well as show some possible applications of approximating parametrized metrics in the problems of words combinatorics.

We introduce a new variation on the domination theme which we call vertex domination as reducing waste of time in transportation planning and optimization of transport routes. We determine the vertex domination number $\gamma_v$ for several classes of fuzzy graphs. The bounds is obtained for it. In fuzzy graphs, monotone decreasing property and monotone increasing property are introduced. We prove both of the vizing's conjecture and the Grarier-Khelladi's conjecture are monotone decreasing fuzzy graph property for vertex domination. We obtain Nordhaus-Gaddum (NG) type results for these parameters. The relationship between several classes of operations on fuzzy graphs with the vertex domination number of them is studied. Finally, we discuss about vertex dominating set of a fuzzy tree by using the bridges and $\alpha$-strong edges equivalence.

This Paper intends to introduce the notion of prime ideals of Intuitionistic fuzzy normed Rings and to establish basic properties related to it. It investigates these notions and shown anew Result using intuinistic fuzzy points and non membership function incorparating with t-norm and s-norm to show aome results of fuzzy prime ideal.

The challenging issues of Computer Network and Databases are not only the intrusion detection but also the reduction of false positive and increase of detection rate. In any intrusion detection system, anomaly detection mainly focuses on modeling the normal behavior of the users and detecting the deviations from normal behavior which are assumed to be potential intrusions or treat. Several techniques have already been successfully tried for this purpose. However, the normal and suspicious behavior are hard to predict as there is no precise boundary differentiat-ing one from another. Here rough set theory and fuzzy set theory come into the picture. In this article, a hybrid approach based on rough set theory and intuitionistic fuzzy set theory is pro-posed for the detection of anomaly. The proposed approach is a classification approach which takes the advantages of softness properties both rough and fuzzy set theory to deal with uncer-tainty in the dataset. The algorithm classifies the data instances in such a way that they can be expressed using natural language. The experimental results with a real world dataset and a syn-thetic dataset show that the proposed algorithm has normal true positive rates of 91.989% and 96.99% and attack true positive rates of 91.289% and 96.29% respectively

This paper provides a comprehensive analysis of food security in Sudan by adopting a unique approach of Hesitant Fuzzy Entropy (HFE) analysis to discern the key determinants influencing food security levels and aligning the findings with the Integrated Food Security Phase Classification (IPC) framework. The research utilized a dataset comprising 32 crucial variables related to food security assessment. Employing entropy values, weight coefficients, heatmaps, and scatterplots, the analysis aimed to unravel the intricate distribution of food security levels among Sudanese individuals in our study area. The study reveals that approximately 26% of the Sudanese population in our study region is poised to experience food security, with an additional 24% categorized as marginally food secure. Moreover, an estimated 35% are expected to confront moderate food insecurity, while 15% are projected to face severe food insecurity between January and June 2024. Anticipations for the period from January 2024 to June 2024 project more than 15 million individuals to encounter IPC Phase 3 and fall under moderately or severely food insecure levels. These findings emphasize the urgent need for both short-term humanitarian aid and long-term strategies to address Sudan's deepening food insecurity crisis.

Quantitative and qualitative fuzzy measures have been proposed to hesitant fuzzy sets (HFSs) from different points. However, few of the existing HFSs fuzzy measures refer to the grey relational analysis (GRA) theory. Actually, the GRA theory is very useful in the fuzzy measure domain, which has been developed for such the intuitionistic fuzzy sets. Therefore, in this paper, we apply the GRA theory to the HFSs and interval-valued hesitant fuzzy sets (IVHFS) domain. We propose the HFSs grey relational degree, HFSs slope grey relational degree, HFSs synthetic grey relational degree and IVHFSs grey relational degree, which describe the closeness, the variation tendency and both the closeness and variation tendency of HFSs and closeness of IVHFSs, respectively, greatly enriching the fuzzy measures of HFSs. Furthermore, with the help of the TOPSIS method, we develop the grey relational based MADM methodology to solve the HFSs and IVHFSs MADM problems. Finally, combined with two practical MADM examples about energy policy selection with HFSs information and emergency management evaluation with IVHFSs information, we obtain the most desirable decision results, and compared with the previous methods, the validity, effectiveness and accuracy of the proposed grey relational degree for HFSs and IVHFSs are demonstrated in detail.

In this paper, we employ fuzzy Sumudu transform for solving system of linear fuzzy differential equations with fuzzy constant coefficients. The system with fuzzy constant coefficients is interpreted under strongly generalized differentiability. For this purpose, new procedures for solving the system are proposed. A numerical example is carried out for solving system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.

Public-private partnership (PPP) is a prominent tool for sustainable infrastructure development. However, the positive contributions of PPPs towards attainment of sustainable, climate resilience and zero carbon infrastructure projects are hampered by poor financial risk management. This problem is more prevalent in developing countries like Ghana where private investment inflow has plummeted due to COVID-19 recession and poor project performance. Thus, this study aims at assessing the key financial risk management strategies in ensuring sustainable PPP infrastructure projects in Ghana. The study utilised primary data from PPP practitioners in Ghana solicited through survey questionnaires. Factor analysis, mean scores and fuzzy synthetic analysis are the data analysis techniques for this study. The results revealed sustainable and green funding models, effective cost reduction initiatives, competent team with committed leadership, and emerging technologies and regulations constitute the key strategies to manage financial risks of sustainable PPP infrastructure projects. Although, future studies must expand the scope of data gathering, the findings of the study enrichen the theoretical understanding of financial risks in sustainable investments in PPP infrastructures. Relevant remedies that will aid the development of practical financial risk management guidelines are provided in this study for PPP practitioners.

In this paper, $(\alpha,\beta)$-fuzzy sublattices and $(\alpha,\beta)$-fuzzy ideals of a lattice, where $\alpha\in\{ \in_{\gamma}, q_{\delta}, \in_{\gamma}\vee q_{\delta}\}$, $\beta\in\{ \in_{\gamma}, q_{\delta}, \in_{\gamma}\vee q_{\delta},\in_{\gamma}\wedge q_{\delta}\}$, are introduced and studied. In the special case, $(\in_{\gamma}, \in_{\gamma}\vee q_{\delta})$-fuzzy sublattices and $(\in_{\gamma}, \in_{\gamma}\vee q_{\delta})$-fuzzy ideals of a lattice are presented and their characterizations by three level sublattices and ideals are given.

Two well-known drawbacks in fuzzy clustering are the requirement of assign in advance the number of clusters and random initialization of cluster centers.; the quality of the final fuzzy clusters depends heavily on the initial choice of the number of clusters and the initialization of the clusters, then it is necessary to apply a validity index to measure the compactness and the separability of the final clusters and run the clustering algorithm several times. We propose a new fuzzy C-means algorithm in which a validity index based on the concepts of maximum fuzzy energy and minimum fuzzy entropy is applied to initialize the cluster centers and to find the optimal number of clusters and initial cluster centers in order to obtain a good clustering quality, without increasing time consumption. We test our algorithm on UCI machine learning classification datasets comparing the results with the ones obtained by using well-known validity indices and variations of FCM using optimization algorithms in the initialization phase. The comparison results show that our algorithm represents an optimal trade-off between the quality of clustering and the time consumption.

The multiphase motors due to their reliability find new areas of application in the industry and transportation. Developing of any system with multiphase motors at first requires elaborate model of the system, define control mode and controllers. The model of control system for the six-phase drive is based on its conventional d-q mathematical model and indirect field-oriented control. Simulink model of six-phase drive with indirect field-oriented control and simulated with two types PID and PID fuzzy controllers. The simulation results, reflecting step response and provided speed reference law as well as load application at constant speed, are presented and analyzed. Fuzzy controller with 49 rules is considered and applied. Six-phase electric drive with field-oriented control at well-tuned PID controller has good step response specifications: settling time 0.13 s at starting without load, step response has no overshoot, small about 1 % short time decrease of speed at load of 5 Nm application. The system employing PID fuzzy controller shows slightly better results in response to torque application: the decrease in speed 1 % is eliminated in shorter time. Simulation results indicate the robustness of both systems with six-phase drive to disturbance and provide high quality transient specifications at determined reference speed.

In this paper, we first define the concepts of r-fuzzy soft α-open (semi-open and δ-open) sets on fuzzy soft topological spaces based on the article Aygunoglu et al. (Hacet. J. Math. Stat., 43 (2014), 193-208), and the relations of these sets with each other are established. In addition, we introduce the concepts of fuzzy soft δ-closure (δ-interior) operators, and study some properties of them. Also, the concept of r-fuzzy soft δ-connected sets is introduced and studied with help of fuzzy soft δ-closure operators. Thereafter, we define the concepts of fuzzy soft α-continuous (β-continuous, semi-continuous, pre-continuous and δ-continuous) functions, which are weaker forms of fuzzy soft continuity, and some properties of these functions along with their mutual relationships are discussed. Moreover, a decomposition of fuzzy soft α-continuity and a decomposition of fuzzy soft semi-continuity is obtained. Finally, as a weaker form of a fuzzy soft continuity, the concepts of fuzzy soft almost (weakly) continuous functions are defined, and some properties are specified. Additionally, we explore the notion of continuity in a very general setting called, fuzzy soft (L, M, N, O)-continuous functions and a historical justification is introduced.

In this research paper an algorithm for the derivation of methods based on theorems and axioms of fuzzy logic is presented, analyzed and applied. This new proposed procedure generates fuzzy methods and evaluates the value of fuzzy propositions through fuzzy implication. The new implications of the family should satisfy a number of axioms. Also, we denote the conditions in order to satisfy the maximum number of axioms. Moreover, authors state and prove theorems focusing on fuzzy implication, observing the rule: the fuzzy function of fuzzy implication is strong and that lead to fuzzy negation. In addition, the optimal number of repetitions is calculated according to the expected truth value. The formulas produced are verified through the use of temperature and humidity values over a certain period of time and in a certain geographical area in Greece. The basic steps of the methodology are the fuzzification of the data given ​​using four membership degree functions and the application of the membership degrees of temperature and humidity values on a new type of fuzzy implication. Finally, we observed that the isosceles trapezium gave the best results and the type of fuzzy implication can be effectively applied.

We examined how combinations of corporate social responsibility (CSR) activities lead to high performance in Korean companies. This study addressed two related questions to expand our limited knowledge in this area. The first was what combinations of CSR activities achieve high performance. The second was to identify how CSR activities form an interdependent system, depending on different corporate situations. Korean Economic Justice Institute index data, from 2012 to 2018, were used with fuzzy set qualitative comparative analysis, and the results revealed several effective CSR activity factor combinations under given strategies and management environments. Companies with high performance exhibit complementarity between social contribution, environmental management, fairness, and employee satisfaction. By contrast, companies with low corporate performance show no complementarity between relatively unrelated activity factors. For companies whose CSR activities lead to low financial performance, most of the causal pathways focused only on activities at the primary stakeholder level, with weak diversity of CSR activities’ combinations at the primary and secondary stakeholder levels. These results indicate not only the appropriateness of CSR activity factor combinations for companies’ strategy and management environment contexts, but also their effectiveness, and are expected to provide companies with significant implications for CSR activities.

In this article, we first introduced new types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) and discussed some topological properties of them. Thereafter, we defined a stronger form of (r,s)-gfsc sets called (r,s)-g*fsc sets and investigated some of its features. Moreover, we showed that (r,s)-fsc set → (r,s)-g*fsc set → (r,s)-gfsc set, but the converse may not be true. In addition, we explored new types of fuzzy generalized mappings between double fuzzy topological spaces (U, τ, τ*) and (V, η, η*), and the relationships between these classes of mappings were examined with the help of some illustrative examples. Finally, some new types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.

The term fuzzy refers to things that are unclear or vague. In the real world, we often encounter a situation where we cannot determine whether the state is true or false, and fuzzy logic allows for more flexible reasoning. This is a form of multivalued logic where the truth values ​​of variables can be any real number between 0 and 1, as opposed to Boolean logic where the logical values ​​can only be 0 or 1. Fuzzy logic is therefore a problem-solving technique used to evaluate all available information and thus make the best decisions. When applied to marketing, fuzzy logic allows treating customers in an individual and personalized way, instead of being fully identified within a particular market segment. Fuzzy marketing considers the degree to which a customer belongs to certain segments and subsequently allows them to be targeted with messages that engage them emotionally. To better understand the application and importance of fuzzy logic in marketing strategy, we developed a systematic review of the bibliometric literature (LRSB). It was possible to create a connection between these concepts, marketing and fuzzy logic, to increase the efforts of marketing professionals to achieve competitiveness in the unpredictable business environment.

In this paper, the concept of fuzzy locally convex spaces generated by a family of fuzzy seminorms is introduced. We prove that a Minkowski functional of zero neighborhoods generates a seminorm and finally deduce that the topology generated by the family of seminorms coincides with that of the Minkowski functional.

In this article, the concept of fuzzy $(\sigma,\mathcal{Z})$-contractive mapping has been introduced in fuzzy metric spaces which is an improvement over the corresponding concept recently introduced by Shukla et al. [Fuzzy Sets and system. 350 (2018) 85--94]. Thereafter, we utilized our newly introduced concept to prove some existence and uniqueness theorems in $\mathcal{M}$-complete fuzzy metric spaces. Our results extend and generalize the corresponding results of Shukla et al.. Moreover, an example is adopted to exhibit the utility of newly obtained results.

Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function is the better way to consider the semantics of the linguistic terms during the evaluation process. In the present paper, we first define some new modified operational laws for Fermatean fuzzy linguistic numbers (FFLNs) based on linguistic scale function (LSF) to overcome the shortcomings of the existing operational laws and prove some important mathematical properties of them. Based on it, the work defines several new aggregation operators (AOs), namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geometric (FFLWG) operator, the FFL-ordered weighted averaging (FFLOWA) operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator under FFL environment. Several properties of these AOs are investigated in detail. Further, based on these operators, a multiple attribute group decision-making (MAGDM) approach with FFL information is developed. Finally, to illustrate the effectiveness of the present approach, a real-life supplier selection problem is presented where the evaluation information of the alternatives is given in terms of FFLNs.

Considering the unquestionable role of education in economic development, it has an impact at a macroeconomic level—contributing to enhancing productivity and innovation, reducing poverty and promoting social cohesion—and at a personal level—ensuring the improvement of knowledge, skills and individual capabilities and promoting social values like empowerment and equality. Notably, quality education is recognized as one of the Sustainable Development Goals (SDGs), which, jointly with other behaviors and attitudes, could impact the development of societies in other fields like health and well-being, cultural preservation, environmental sustainability and even peace and stability—all of them also listed as SDGs. However, the capacity, or not, to reach higher levels of compliance with quality in education (SDG 4) varies from country to country, according to the 2023 Sustainable Development Report results. Thus, the present study used a fuzzy set qualitative comparative analysis to assess the conditions for attaining higher levels of quality education based on the different indicators used to measure SDG 4. The analysis will allow comparisons of results among different countries and provide information about the initiatives that could be relevant to increasing quality education worldwide and for policymakers.

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

This paper analyzes the potential strategies for a bank merger from a Sustainable Development Goals (SDG) perspective, focusing on three key criteria: profitability, market share, and service quality. In the short-term, the merged bank should prioritize optimizing financial performance through cost management, revenue stream identification, and risk management practices. Market share expansion can be achieved through targeted customer acquisition and retention efforts, market research, and competitive analysis. Service quality can be enhanced through improved customer service, efficient complaint resolution processes, and leveraging technology. These short-term plans align the merged bank's operations with the identified criteria and promote responsible banking practices that contribute towards the SDGs. In the long-term, the merged bank should focus on diversifying revenue streams, expanding its customer base, and optimizing cost structure. Long-term strategies should include establishing a strong brand presence, customer loyalty programs, and continuous improvement in service quality. The paper emphasizes the importance of monitoring progress, making necessary adjustments, and aligning with SDGs for sustained profitability and long-term success in the marketplace. The findings of this study provide valuable insights for banks considering a merger and highlight the significance of considering SDGs in their strategic planning.

The Fuzzy Transportation Problem (FTP) represents a significant extension of the Classical Transportation Problem (TP) by introducing uncertainly and imprecision into the parameters involved. Various algorithms have been proposed to solve the FTP, including fuzzy linear programming, metaheuristic algorithms and fuzzy mathematical programming techniques combined with Artificial Neural Networks. This paper presents the application of Trigonometric Acceleration Coefficients-PSO (TrigAc-PSO), a variation of the Classical Particle Swarm optimization algorithm, which is an innovative algorithm originally developed for solving the TP. TrigAC-PSO, has demonstrated remarkable success in optimizing various problem domains in crisp environments.

In this paper, improved matrix Reduction Method is proposed for the solution of fuzzy transportation problem in which all inputs are taken as fuzzy numbers. Since ranking fuzzy number is important tool in decision making, Fuzzy trapezoidal number is converting in to crisp set by using Mean techniques and solved by proposed method for fuzzy transportation problem. We give suitable numerical example for unbalanced and compare the optimal value with other techniques. The Result shows that the optimum profit of transportation problem using proposed technique under robust ranking method is better than the other method. Novelty: The numerical illustration demonstrates that the new projected method for managing the transportation problems on fuzzy algorithms.

In this manuscript, we first introduce some properties of r-fuzzy soft α-open sets in fuzzy soft topological spaces based on the manuscript Aygunoglu et al. (Hacet. J. Math. Stat. 2014, 43, 193-208). In addition, we define the concepts of fuzzy soft α-closure (α-interior) operators, and investigate some properties of them. Furthermore, the concept of r-fuzzy soft α-connected sets is defined and characterized with help of fuzzy soft α-closure operators. Thereafter, we introduce and study the concepts of fuzzy soft almost (weakly) α-continuous mappings, which are weaker forms of fuzzy soft α-continuous mappings, and we discuss some properties of fuzzy soft α-continuity. Moreover, we establish that fuzzy soft α-continuity → fuzzy soft almost α-continuity → fuzzy soft weakly α-continuity, but the converse may not be true. It is also we show that the composition is fuzzy soft almost α-continuous mapping if, is fuzzy soft α-continuous mapping and is fuzzy soft almost continuous mapping. Finally, some new types of compactness via r-fuzzy soft α-open sets are defined, and the relationships between them are examined.

In India, the divorce rate is rising year after year. Divorces are thought to have increased by more than a factor of two during the past two decades. India has great cultural diversity, and each of its states has something unique to offer. The divorce rate in India, which differs from state to state, is among the most frequently discussed subjects. More than 30% of marriages end in divorce in big cities like Delhi, Mumbai, Chennai, and Bangalore. Divorce applications have nearly tripled in the past few years in cities like Delhi, Bangalore, Mumbai, Kolkata, and Lucknow. In India, the divorce rate has increased, especially in small cities. Hence, the reasons behind divorce in India were explored in this article. In order to analyze the causes of divorce, the current study aimed to combine the critical components of TOPSIS and COPRAS methodologies in a fuzzy environment. Additionally, it is shown that a comparison study may pinpoint the characteristics that influence divorces the most.

Recently, new advanced techniques have been proposed to improve the quality of smart grids that use intermittent renewable energy sources. One of the most effective techniques is active filtering, which utilizes a power electronic converter in the smart load. This technique has the potential to enhance the power quality of the supply voltage by minimizing current harmonics, which is crucial. In this article, we propose a new command intelligence system based on Fuzzy PI fractional (fuzzy FOPI) and GA to control the harmonic currents generated by an active filter powered by a wind system.

In fuzzy group decision making problems and fuzzy shortest path problems, the addition and subtraction are the basic problems. For the mixed normal fuzzy numbers and trapezoidal fuzzy numbers, the addition and subtraction operations are approximated by the normal fuzzy numbers in this paper. The behaviors of approximated normal fuzzy numbers are the same as those of the normal distributions from the viewpoint of probability. An application of the addition and subtraction operations of mixed fuzzy numbers to the fuzzy sample mean is also proposed.

This study aimed to identify the influencing factors that drive the adoption of smart construction technologies by highway construction companies. Using expert interviews and expert scoring, interview data were collected from 25 experts in the field, and the TOSE framework was proposed based on the TOE framework, identifying four dimensions and fourteen influencing factors. The results were analyzed using the Fuzzy-DEMATEL-ISM method, and the findings were then summarized according to the evaluation criteria to determine the validity of the fourteen hypotheses and the extent to which they drive the adoption of intelligent construction technologies by motorway construction companies. The findings of this paper will be of great value to decision-makers and participants in highway construction companies, as well as to other companies in the construction industry, in their decision to adopt smart construction technologies.

The present study is to address performance of the dairy supply chain and emphasizes the significance of reliability of the chain as a fundamental and critical attribute for fulfilling the safety requirements. In order to evaluate the performance of the dairy supply chain, the present study utilizes the reliability attribute, which is an essential and informative system performance indicator. The study considers not only the inputs and outputs but also internal activities and relationships between customers, manufacturers, and suppliers. To minimize calculations and resolve uncertainties and vagueness that may be experienced in the performance evaluation process, this study proposes the use of the Fuzzy Inference System (FIS) approach and evaluates the reliability at each level of the supply chain: supply, manufacturing, and distribution. Combining the reliability of different levels, the study finally calculates the reliability of the entire supply chain. The proposed methodology offers a practical approach for evaluating the reliability performance of a dairy supply chain and can be easily extended to other industries as well. To verify the proposed methodology, a real case in the Iranian dairy industry is chosen to be studied. Results indicate that the proposed methodology can effectively identify bottlenecks or weaknesses in the dairy supply chain and help develop effective strategies to address them. Analyzing factors influencing supply chain reliability can optimize operations, reduce costs, and improve the overall quality of dairy product quality delivered to consumers.

Flash flood is one of the most significant natural disasters in China, particularly in mountainous area, causing heavy economic damage and casualties of life. Accurate risk assessment is critical to an efficient flash flood management. There are more than 530,000 small watersheds in 2058 counties in China where flash flood should be prevented. In practice, with limited fund and different risk levels, the priorities of each small watershed for flash flood prevention and control are also needed for an efficient flash flood management. This paper, take Licheng county in China as an example, aims to give out these priorities for management. First, sensitive indexes are identified among index system, which includes 9 indexes based on underlying surface characteristics of small watershed in hilly region. Second, the range of each index and the rank division of each index for evaluation are determined. Based on the rank divisions for evaluation, the flash flood risk grade eigenvalue (H) is calculated by Variable Fuzzy Method (VFM ) using 1000 samplings generated by Latin hypercube sampling method. Third, the key sensitivity factors that affect flash flood risk grade eigenvalue (H) are assessed by two different global sensitivity analysis methods -- stepwise regression analysis and mutual entropy. Both results indicate that watershed slope (S) is the most sensitive factor; the second is antecedent precipitation index (CN); while other factors are slightly different sensitive in sequence. This study shows that stepwise regression analysis and mutual information analysis are appropriate for the sensitivity analysis of mountain flash flood risk. Finally, based on watershed slope (S), the priorities of flash flood prevention and control of 119 small watersheds in Licheng county are given out.

In the present study. At first, some properties of r-fuzzy soft β-closed sets are introduced on fuzzy soft topological spaces based on the paper Aygunoglu et al. (Hacet. J. Math. Stat. 2014, 43, 193-208). Also, we define the closure and interior operators with respect to the classes of r-fuzzy soft β-closed and r-fuzzy soft β-open sets, and investigate some of their properties. In addition, the concept of r-fuzzy soft β-connected sets is introduced and characterized with help of fuzzy soft β-closure operators. Thereafter, some properties of a fuzzy soft β-continuity are studied. Furthermore, we introduce and study the concepts of fuzzy soft almost (weakly) β-continuous functions, which are weaker forms of a fuzzy soft β-continuity. Also, the relationships between these classes of functions are specified with the help of some illustrative examples. Finally, we explore new types of fuzzy soft functions called, fuzzy soft β-irresolute (strongly β-irresolute, β-irresolute open, β-irresolute closed and β-irresolute homeomorphism) functions, and discuss some properties of them. Also, we show that fuzzy soft strongly β-irresolute → fuzzy soft β-irresolute → fuzzy soft β-continuity, but the converse may not be true.

This paper has a twofold objective. The first aim is to present a comprehensive bibliographical analysis of journal articles and book chapters on fuzzy-random option pricing (FROP) over the WoS and SCOPUS databases. It follows PRISMA criteria and takes special care of developments in continuous time. Thus, we described the principal findings about the research streams, outlets and authors of this topic and lets us suggest further research. The second contribution is motivated by the fact that the bibliographical revision has identified a lack of developments on equilibrium models on the yield curve. This question motivates extending Vasicek’s yield curve equilibrium model to introduce fuzziness in the parameters that govern interest rate movements (speed of reversion, equilibrium short-term interest rate, and volatility). Likewise, this paper develops an empirical application on the term structure of fixed income public bonds with the highest credit rating in the Euro area.

This paper presents a novel method of restoring the electron beam (EB) measurements that are degraded by linear motion blur. This is based on a Fuzzy Inference System (FIS) and Wiener inverse filter, together providing autonomy, reliability, flexibility and real-time execution. This system is capable of restoring highly degraded signals without requiring the exact knowledge of EB probe size. The FIS is formed of three inputs, eight fuzzy rules and one output. The FIS is responsible to monitor the restoration results, grade their validity and choose the one that yields to a better grade. These grades are produced autonomously by analyzing results of Wiener inverse filter. To benchmark the performance of the system, ground truth signals obtained using an 18 um wire probe are compared with the restorations. Main aims are therefore a) Provide unsupervised deblurring for device independent EB measurement; b) Improve the reliability of the process; c) Apply deblurring without knowing the probe size. These, further facilitates the deployment and manufacturing of EB probes and probe independent and accurate EB characterization. It also makes restoration of previously collected EB measurements easier, where the probe sizes are not known or recorded.

This paper aims to investigate impact of employees’ gender on OCB as per the employees’ perception in Jordanian governmental hospitals. A convenient sample of 126 employees working in the three main governmental hospitals in north of Jordan has been taken for the purpose of this study. The collected data includes linguistic terms that suffer from uncertainty which, in turn, cannot be dealt with traditional numerical values. The result prove that gender impact on OCB has shown statistically significant differences at (α=0.05) as far as altruism, courtesy, and civic virtue are concerned; and this variable stands in favor of males with the total score of 0.011%. Similarly, as far as the effect of age factor on OCB is concerned, there have been statistically significant differences at (α=0.05) in relation to courtesy, sportsmanship, and civic virtue with the total score of 0.27%. Finally, the results provide a baseline data for further studies which may contribute more significant in the field of OCB.

Study of differential equation theory has come a long way with applications in the various fields. In 1961, Zygmund and Calderón introduced the notion of derivatives on metric Lr which proved to be better in applications than approximate derivatives. But most of the studies involved are on fuzzy set theory, so it seems likely that intuitionistic fuzzy Lr - norm - based derivatives deserve study. In the study, the fuzzy derivative is extended to intuitionistic fuzzy derivatives with respect.to Lr - norm - based derivatives using intuitionistic fuzzy number valued functions. The efficacy of the proposed method is established by proving the associated theorems along with numerical examples. Further, the Cauchy problem is also studied with respect to intuitionistic fuzzy setting.

Given a fuzzy normed space $ \left( X,N \right) $‎, ‎we will introduce the notion of fuzzy near best approximation within a relative distance $ \rho \geq 0 $‎. ‎Some basic properties are characterized and also many examples for illustration are presented‎.

The aim of this expository article is to present recent developments in the centuries-old discussion on the interrelations between several types of domination in graphs. However, the novelty even more prominent in the newly discovered simplified presentations of several older results. Domination can be seen as arising from real-world application and extracting classical results as first described by this article.The main part of this article, concerning a new domination and older one, is presented in a narrative that answers two classical questions: (i) To what extend must closing set be dominating? (ii) How strong is the assumption of domination of a closing set? In a addition, we give an overview of the results concerning domination. The problem asks how small can a subset of vertices be and contain no edges or, more generally how can small a subset of vertices be and contain other ones. Our work was as elegant as it was unexpected being a departure from the tried and true methods of this theory that had dominated the field for one fifth a century. This expository article covers all previous definitions. The inability of previous definitions in solving even one case of real-world problems due to the lack of simultaneous attentions to the worthy both of vertices and edges causing us to make the new one. The concept of domination in a variety of graphs models such as crisp, weighted and fuzzy, has been in a spotlight. We turn our attention to sets of vertices in a fuzzy graph that are so close to all vertices, in a variety of ways, and study minimum such sets and their cardinality. A natural way to introduce and motivate our subject is to view it as a real-world problem. In its most elementary form, we consider the problem of reducing waste of time in transport planning. Our goal here is to first describe the previous definitions and the results, and then to provide an overview of the flows ideas in their articles. The final outcome of this article is twofold: (i) Solving the problem of reducing waste of time in transport planning at static state; (ii) Solving and having a gentle discussions on problem of reducing waste of time in transport planning at dynamic state. Finally, we discuss the results concerning holding domination that are independent of fuzzy graphs. We close with a list of currently open problems related to this subject. Most of our exposition assumes only familiarity with basic linear algebra, polynomials, fuzzy graph theory and graph theory.

We propose a new Mamdani fuzzy rule-based system in which the fuzzy sets in the antecedents and consequents are assigned in a discrete set of points and approximated by using the extended inverse fuzzy transforms, whose components are calculated by verifying that the dataset is sufficiently dense with respect to the uniform fuzzy partition. We test our system in the problem of spatial analysis consisting in the evaluation of the liveability of residential housings in all the municipalities of the district of Naples (Italy). Comparisons are done with the results obtained by using trapezoidal fuzzy numbers in the fuzzy rules.

Nowadays, model checking is applied as an accurate technique to verify software systems. The main problem of model checking techniques is the state space explosion. This problem occurs due to the exponential memory usage by the model checker. In this situation, using meta-heuristic and evolutionary algorithms to search for a state in which a property is satisfied/violated is a promising solution. Recently, different evolutionary algorithms like GA, PSO, etc. are applied to find deadlock state. Even though useful, most of them are concentrated on finding deadlock. This paper proposes a fuzzy algorithm in order to analyze reachability properties in systems specified through GTS with enormous state space. To do so, we first extend the existing PSO algorithm (for checking deadlocks) to analyze reachability properties. Then, to increase the accuracy, we employ a Fuzzy adaptive PSO algorithm to determine which state and path should be explored in each step to find the corresponding reachable state. These two approaches are implemented in an open-source toolset for designing and model checking GTS called GROOVE. Moreover, the experimental results indicate that the hybrid fuzzy approach improves speed and accuracy in comparison with other techniques based on meta-heuristic algorithms such as GA and the hybrid of PSO-GSA in analyzing reachability properties.

Abstract: Wildfires in forest ecosystems exert substantial ecological, economic, and social impacts. The effectiveness of fire management hinges on precise pre‐fire risk assessments to inform mitigation efforts. This study aims to investigate the relationship between predictions from pre‐fire risk assessments and outcomes observed through post‐fire burn severity analyses. In this study, forest fire risk was assessed with the Fuzzy Analytical Hierarchy Process, in which fire behavior factors were used as input. The degree of burn was determined using the Random Forest method using 11519 training points and 400 test points on Sentinel‐2 satellite images in three different classes. According to the results obtained from 266 selected test points located within the forest boundaries, all primary factors showed an increased effect in areas with high burn severity. Climate, in particular, emerged as the most influential factor, accounting for 52% of the overall impact. However, in cases of high fire severity, climate proved to be the most effective risk factor, ac‐counting for 67%. It followed by topography with 50% accuracy at high fire intensity. In the risk assessment is based on the FAHP method, climate was assigned the highest weight value among other factors with 32.2%. Topography emerged as the second most effective risk factor with 27 %. To evaluate the results more comprehensively both visually and statistically, two regions with different stand canopy characteristics were selected within the study area. While high burn severity had the highest accuracy in Case 1 area, moderate burn severity had the highest in Case 2 area. During the days when the fire continued, the direction of spread was obtained from MODIS images. In this way, the fire severity depending on the direction of fire progression was also interpreted. Through an analysis of various case studies and existing literature, the research underscores both the strengths and limitations inherent in predicting forest fire behavior‐based pre‐fire risk assessments. Furthermore, it emphasizes the necessity of continuous improvement to increase the success of forest fire management.

Investment management is a common process and practice used for achieving a desirable investment goal or outcome. Investment assessment should be carried out at various stages of project realization in accordance with capital investment volume. Investment risk management implies the effective control of all procedures and monitoring of risks in all phases of the investment project. Because of the reason that a single indicator in probability calculation of achieving optimal return from the investment does not exist, performing sufficiently reliable estimates of the quality of investments becomes a tedious task. There are many indicators, factors, and criteria required for consideration to reach the effective solution of the investment problem. Unfortunately, the systematic variation of economic situations in the marketplace stipulates the continuous and frequent changes of investment conditions and environment in which the investor should act and operate. Hence, the rules required for providing a reasonable quality of investment projects can be based only on investor’s management strategy and rely on investor’s intuition and practice. The importance of classification in investment management and decision making process is undeniable. The objects to be classified are described using assessments in accordance with various criteria which can be both quantitative and qualitative. With a competent formulation of the investment process, both methods are used in parallel. There exist various decision making approaches for the investment management, and simple additive weighting (SAW) is one of the well-known multi-criteria decision making (MCDM) methods aiming to provide an optimal decision for decision maker when solving various real-life problems, and particularly, investment problem. In this paper, fuzzy simple additive weighting (FSAW) method in group decision making is applied to undertake the capital investment expenditure for purchasing cars with the purpose of renting them to the public. The development of existing FSAW method is accomplished and this process involves the sensibility of outcomes to changes in the rate of fuzziness represented with decisions taken. Eventually, the degree of fuzziness involved in an analysis that directly attempts to model the immanent vagueness and imperfectness in particular precedency judgments made, is determined. A numerical example illustrates the importance and effectiveness of the suggested approach with the aim of ranking alternatives and hence, determining the most preferred alternative in MCDM problem.

The purpose of the study is to control the ratio of programs of different genres when forming the broadcast grid in order to increase and maintain the rating of the channel. In the multichannel environment, television rating control consists of selecting such content, ratings of which are completely restored after advertising. A hybrid approach combining the benefits of semantic training and fuzzy relational equations in simplification of the expert recommendation systems construction is proposed. The problem of retaining the television rating can be attributed to the problems of fuzzy resources control. The increase or decrease trends of the demand and supply are described by primary fuzzy relations. The rule-based solutions of fuzzy relational equations connect significance measures of the primary fuzzy terms. Rules refinement by solving fuzzy relational equations allows avoiding labor-intensive procedures for the generation and selection of expert rules. The solution set generation corresponds to the granulation of the television time, where each solution represents the time slot and the granulated rating of the content. In automated media planning, generation of the weekly TV program in the form of the granular solutions provides the decrease of the time needed for the programming of the channel broadcast grid.

Based on the definition of double fuzzy relations, two types of new rough set models are constructed, which are multi-granulation double fuzzy rough sets called optimistic and pessimistic multi-granulation double fuzzy rough sets, and some of their properties were studied. In addition, we study the relationship between optimistic and pessimistic multi-granulation double fuzzy rough sets and double fuzzy rough sets.

The aim of this article is introduced the concept of double framed T-soft fuzzy set (DFT-soft fuzzy set) which is the combination of soft set and fuzzy set. We also defined the notions and apply this concept in BCK/BCI-algebras. By using example, we also discussed the concept of double framed T-soft fuzzy algebra (DFT-soft fuzzy algebra) and double framed B-soft fuzzy algebra (DFB-soft fuzzy algebra) and also investigated their properties. Each double framed T-soft fuzzy algebra is double framed B-soft fuzzy algebra but by using example, we proved that converse may or may not be possible.

The hybridization of machine learning methods with soft computing techniques is an essential approach to improve the performance of the prediction models. Hybrid machine learning models, particularly, have gained popularity in the advancement of the high-performance control systems. Higher accuracy and better performance for prediction models of exergy destruction and energy consumption used in the control circuit of heating, ventilation, and air conditioning (HVAC) systems can be highly economical in the industrial scale to save energy. This research proposes two hybrid models of adaptive neuro-fuzzy inference system-particle swarm optimization (ANFIS-PSO), and adaptive neuro-fuzzy inference system-genetic algorithm (ANFIS-GA) for HVAC. The results are further compared with the single ANFIS model. The ANFIS-PSO model with the RMSE of 0.0065, MAE of 0.0028, and R² equal to 0.9999, with a minimum deviation of 0.0691 (KJ/s), outperforms the ANFIS-GA and single ANFIS models.

Many systems in the manufacturing industry have spatial distribution characteristics, which correlate with both time and space. Such systems are known as distributed parameter systems (DPS). Due to the spatiotemporal coupling characteristics, the modeling of such systems is quite complex. The paper presents a new approach for three-dimensional fuzzy modeling using Simultaneous Perturbation Stochastic Approximation (SPSA) for nonlinear DPS. The Affinity Propagation clustering approach is utilized to dynamically determine the optimal number of fuzzy rules and construct a collection of preceding components for three-dimensional fuzzy models. Fourier space base functions are used in the resulting components of three-dimensional fuzzy models, and their parameters are learned by the SPSA algorithm. The proposed three-dimensional fuzzy modeling technique was utilized on a conventional DPS within the semiconductor manufacturing industry, with the simulation experiments confirming its efficacy.

Several life contingency agreements are based on the assumption that policyholders have impaired life expectancy attributable to factors such as lifestyle, social class, or preexisting health issues. Quantifying two crucial variables, augmented death probabilities and the discount rate of projected cash flows, is essential for pricing such agreements. Information regarding the correct values of these parameters is subject to vagueness and imprecision, which further intensifies if impairments must be considered. This study proposes modelling mortality and interest rates using a generalization of fuzzy numbers (FNs), known as intuitionistic fuzzy numbers (IFNs). Consequently, this paper extends the literature on life contingency pricing with fuzzy parameters, where uncertainty in variables, such as interest rates and death probabilities, is modelled using FNs. While FNs introduce epistemic uncertainty, the use of IFNs adds bipolarity to the analysis by incorporating both positive and negative information regarding actuarial variables. Our analysis focuses on two agreements involving policyholders with impaired life expectancy: determining the annuity payment in a substandard annuity and pricing a life settlement over a whole life insurance policy. In particular, we emphasize modelling interest rates and survival probabilities using triangular intuitionistic fuzzy numbers (TIFNs) owing to their ease of interpretation and implementation.

In a collaborative forecasting task, experts may have unequal authority levels. However, this has rarely been considered reasonably in the existing fuzzy collaborative forecasting methods. In addition, experts may not be willing to discriminate their authority levels. To address these issues, an auto-weighting fuzzy weighted intersection (FWI) fuzzy collaborative intelligence approach is proposed in this study. In the proposed auto-weighting FWI fuzzy collaborative intelligence approach, experts’ authority levels are automatically and reasonably assigned based on their past forecasting performances. Subsequently, the auto-weighting FWI mechanism is established to aggregate experts’ fuzzy forecasts. The theoretical properties of the auto-weighting FWI mechanism have been discussed and compared with those of the existing fuzzy aggregation operators. After applying the auto-weighting FWI fuzzy collaborative intelligence approach to a case of forecasting the yield of a DRAM product from the literature, its advantages over several existing methods were clearly illustrated.

In this paper we address one of the most important topics in the field of Social Networks Analysis: the community detection problem with additional information. That additional information is modeled by a fuzzy measure that represents the possibility of polarization. Particularly, we are interested in dealing with the problem of taking into account the Polarization of nodes in the community detection problem. Adding this type of information to the community detection problem makes it more realistic, as a community is more probably to be defined if the corresponding elements are willing to maintain a peaceful dialogue. The polarization capacity is modeled by a fuzzy measure based on the JDJpol measure of polarization related to two poles. We also present an efficient algorithm for finding groups whose elements are no polarized. Hereafter, we work in a real case. It is a network obtained from Twitter, concerning the political position against the Spanish government taken by several influential users. We analyze how the partitions obtained change when some additional information related to how polarized that society is, is added to the problem.

Manufacturing corporations has the acceptance of the Outsourcing Process (OP) to improve industrial activities as well as to archive the revenue objectives, and with this, Risk Analysis (RA) tools are constantly used to assure expected results. Failure Mode and Effect Analysis (FMEA) is one of preferred RA tools, moreover, it is proven that FMEA adds uncertainty because of the human participation at the RA, afterward it is demonstrated that Pythagorean Fuzzy Dimensional Analysis – FMEA – Value Stream Mapping (PFDA-FMEA-VSM) method removes the uncertainty in RA, likewise it aids to the stakeholders for decision making, giving more advantages improving the use of the resources on the project. This document exhibits a real case scenario in a manufacturing firm applying PFDA-FMEA-VSM method adapted for manufacturing OP. The application of PFDA-FMEA-VSM shows solid RA results, removing the human intervention uncertainty added to the risk ranking, gives advantages to the stakeholders for visualize the main risks in detailed diagram, as well as make easier to take better decisions on where to apply resources and mitigate risks during OP.

Waste heat recovery stands out as a promising technique to tackle both energy shortages and environmental pollution. Currently, this valuable resource, generated from processes like fuel combustion or chemical reactions, is often dissipated into the environment, despite its potential to significantly contribute to the economy. To harness this untapped potential, a travelling-wave thermo-acoustic generator has been designed and subjected to comprehensive experimental analysis. Fifty-two data corresponding to different working conditions of the system were extracted to build ANN, ANFIS and ANN-PSO models. Evaluation of performance metrics reveals that the ANN-PSO model demonstrates the highest predictive accuracy (R^2=0.9959), particularly in relation to output voltage. This research demonstrates the potential of machine learning techniques for the analysis of thermo-acoustic systems. By doing so, it is possible to get an insight into nonlinearities inherent to thermo-acoustic systems. This advancement empowers researchers to forecast the performance characteristics of alternative configurations with a heightened level of precision.

In the realm of construction industry, the management of claims constitutes a pervasive and multifaceted issue, with potential repercussions extending to project delays, cost overruns, work suspensions, and, in extreme cases, project termination. This challenge is a significant and unavoidable hurdle due to the unique features of construction projects, which are complex, involve many stakeholders and come with inherent risks. To address this complex issue, it becomes imperative to undertake a comprehensive appraisal of the claims management procedures employed within the industry, culminating in the presentation of findings within a risk-based framework. The overarching objective of this endeavour is threefold: firstly, to discern the pivotal attributes that affect each category of construction claims; secondly, to establish a coherent decision-making paradigm for the effective administration of such claims; and finally, to provide data that can be harnessed to either address concerns related to claims or enhance the effectiveness of the claims administration process. Keeping this in mind, this study serves to evaluate the factors associated with claim management gathered from a wide overview of literature, encompassing a range of construction projects, varying in terms of types, sizes/capacities and contractual arrangements. Hence, it advanced a refined method within the domain of fuzzy group decision-making, denoted as the Modified Fuzzy Group Decision-Making Approach (FGDMA) in addition to extensive statistical analysis using SPSS.V.25 software. They were applied to assess, analyze and prioritize claim about 108 claim management factors based on the responses obtained from the comprehensive questionnaire survey involving 104 industry professionals. This multi-faceted approach, which combines the insights from previous publications, along with the collective experience of the surveyed professionals with the analytical capabilities of the FGDMA- Statically Factor Analysis, reinforces the robustness and practical applicability of proposed methodology within the context of construction claims management.

In traditional finance, option prices are typically calculated using crisp sets of variables. However, in a proposed new approach, the assumption is made that these parameters have a degree of fuzziness or uncertainty associated with them. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. To determine the belief degree associated with a particular option price, an interpolation search algorithm was proposed recently[1]. Interpolation is a mathematical technique used to estimate values between known data points. In this case, the algorithm is applied to determine the belief degree associated with a specific option price within the range of possible prices. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions. It allows them to consider their risk preferences and beliefs about the uncertain parameters when selecting an option price. In this paper, we will review a unified framework for combining fractional Brownian motion with fuzzy processes and obtain a joint measure space. We start by constructing a product measure space that captures the randomness and fuzziness inherent in the respective processes. We begin with the usual Kolmogorov filtered probability space (Ω, F, ℙ), where ℙ represents the probability measure, Ω is the set of all possible outcomes or states that a random process can take and {Ft, t ∈ [0, T]} is an information filtration. We will review the work of Merton (1976) on option pricing when the underlying stock returns have jumps [2] and expand it to fuzzy fractional processes.

This study evaluated the ranking of comprehensibility of the pictograms for judo, taekwondo, boxing, and wrestling used in the six games from the 27th Sydney Olympics in 2000 to the 32nd Tokyo Olympics in 2021. The evaluation was done using the Fuzzy TOPSIS method, one of the multi-criteria decision-making methodologies commonly used in economics and others fields. The results are as follows. The first, pictograms from the 2008 Beijing Olympics ranked first in three sports: taekwondo, boxing, and wrestling, but there were no pictograms that consistently ranked first or sixth in all sports. Second, the result of the sensitivity analysis shows a possibility that the ranking will be reversed if the weight of the evaluation factors changes, but in the 1000-time repetitive prediction, the better the evaluation ranking, the closer the value of the priority ranking to the ideal solution on average even if the weight changes.

In recent years, new metaheuristic algorithms have been developed taking as reference the inspiration on biological and natural phenomena. This nature-inspired approach for algorithm development has been widely used by many researchers in solving optimization problem. These algorithms have been compared with the traditional ones algorithms and have demonstrated to be superior in complex problems. This paper attempts to describe the algorithms based on nature, that are used in fuzzy clustering. We briefly describe the optimization methods, the most cited nature-inspired algorithms published in recent years, authors, networks and relationship of the works, etc. We believe the paper can serve as a basis for analysis of the new are of nature and bio-inspired optimization of fuzzy clustering.

Sustainable Humanitarian logistics is gaining attention due to increased disasters. It involves various operations to support people's survival efforts. Key characteristics include unpredictable demand, sudden large demand volumes, high stakes in delivery timeliness, and limited resources. However, the complexity and unpredictability of disaster scenarios necessitate robust and adaptable performance measurement models to evaluate the effectiveness of sustainable humanitarian relief logistics (SHRL). This study proposes a novel performance measurement model for sustainable humanitarian logistics and supply chains that integrates the Fuzzy Delphi Method (FDM) and Fuzzy Decision-Making Trial and Evaluation Laboratory (Fuzzy-DEMATEL) method. In this research, using 115 articles focused on sustainable humanitarian logistics and supply chains, crisis management, and humanitarian aid, this research identified 25 key performance indicators (KPIs) in the initial phase. Following the implementation of FDM, 19 KPIs were identified as crucial for further analysis. These KPIs were then divided into four distinct categories: "Quality," "Accountability," "Operational Excellence," and "Sustainability". Initially, FDM is utilized to reach a consensus among experts concerning KPIs for humanitarian logistics and supply chains. By incorporating the inherent uncertainty and vagueness in expert judgments, FDM refines the list of key performance indicators that reflect the real-life conditions and constraints in disaster operations. Finally, the fuzzy DEMATEL approach was used to analyze interrelationships among factors, identifying cause-and-effect behavior and ranking them, forming a robust theoretical framework. The study concludes with the development of a comprehensive performance measurement model that facilitates the strategic planning and operational assessment of humanitarian organization operations. The integration of FDM and fuzzy DEMATEL methods offers multiple perspectives for decision-making and helps stakeholders identify critical areas for improvement. Based on the acquired results, the KPIs attached to the Quality (P1) aspect of the proposed framework have gained significant importance and main cause in the cause-and-effect relationship which impacts and is helpful to improve the performance of humanitarian organizations in all phases of disaster management. The KPIs prompt delivery (D1), and delivery accuracy (D2) are more significant, while capacity building and training (D19) and delivery compliance (D15) are least significant in SHRL scenarios. This research is expected to support humanitarian organizations in enhancing their capabilities, thereby improving the effectiveness and efficiency of aid delivery in disaster-stricken areas.

The circular supply chain was applied to many industries in the past studies, whereas the rubber recycling industry has not been explored in detail yet. Therefore, this study indentified the key factors of the circular supply chain used in remanufactured products, thereby perfecting its framework. This study put forward 5 aspects and 19 criteria for reference, so that companies in the rubber recycling industry are able to clearly know the direction of implementation when con-structing the circular supply chain for remanufactured products. This study integrated expert opinions with the fuzzy Delphi method and the fuzzy decision making trial and evaluation laboratory proposed key factors, and performed the ranking of importance. The results have displayed that key aspects include the circular business model (A3), increasing the value of resources in the supply chain (A4), and risk management of the circular supply chain (A2). The factors that the rubber recycling industry needs to pay attention to are: optimizing the production process (C2), sharing data in the product lifecycle (C4), effectively tracking and recycling products (C5), redesigning remanufactured products (C13), enhancing resource efficiency (C16), and identifying waste composition and separating materials (C14) . Based on the abovementioned, we had a discussion in this study.

Decomposed fuzzy sets are the resent extension of intuitionistic fuzzy sets by incorporating functional and dysfunctional points of views to the definition of membership functions. This paper extends the Technique of Order Preference Similarity to the Ideal Solution (TOPSIS) method to the Decomposed Fuzzy TOPSIS (DF TOPSIS) method and applies it to a multi-criteria risk-based supplier selection problem under fuzziness. DF TOPSIS involves finding a positive ideal solution and a negative ideal solution and measuring the distance of each alternative to these solutions. The final ranking is obtained based on the proportion of distances to the positive and negative ideal solutions. The developed DF TOPSIS method incorporates the accuracy and consistency of expert judgments, enhancing the decision-making process. A sensitivity analysis is also presented in order to show the robustness of the obtained rankings by DF TOPSIS.

Two representable substructural logics ${\rm {\bf UL}}_\omega $ and ${\rm {\bf IUL}}_\omega $ are logics for finite UL and IUL-algebras, respectively. In this paper, the standard completeness of ${\rm {\bf UL}}_\omega $ and ${\rm {\bf IUL}}_\omega $ is proved by the method developed by Jenei, Montagna, Esteva, Gispert, Godo and Wang. This shows that ${\rm {\bf UL}}_\omega $ and ${\rm {\bf IUL}}_\omega $ are substructural fuzzy logics.

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.

With the increasing use of automatic transmissions in passenger vehicles, there is a growing need for improved gear shifting control strategies that aim to enhance performance and fuel efficiency. This paper introduces a knowledge-based fuzzy control system designed specifically for automatic transmissions in light vehicles. The proposed system utilizes a fuzzy inference system as the controller, enabling the emulation of the driver’s perceptions during the gear shifting process. Consequently, the input signal consists of variables that are either sensitive to or observable by the driver, while the output represents the selected gear. The paper evaluates three distinct control strategies, each based on different inputs. These inputs include the longitudinal velocity of the vehicle, the angular velocity of the engine, or a combination of both, along with the time-derivative of the throttle valve opening. Through the evaluation, it is observed that the combination of inputs yields significantly improved performance. Therefore, the methodology presented in this paper demonstrates that the combined input approach is more effective for gear shifting control.

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. In this case, the mutation parameter is dynamically moved during the evolution process by using a shadowed and general type-2 fuzzy systems. The main idea of this work is to make a performance comparison between using shadowed and general type 2 fuzzy systems as controllers of the mutation parameter in differential evolution. The performance is compared with the problem of optimizing fuzzy controllers for a D.C. Motor. Simulation results show that general type-2 fuzzy systems are better when higher levels of noise are considered in the controller.

Digital transformation, organizational resilience, and agility are now becoming one of the keys to meeting the competitive challenges of modern organizations. It is no surprise that digital transformation and digital technologies have also begun to significantly impact the energy industry, moving towards improving the sector's profitability and efficiency. However, to navigate through the difficult process of digital transformation in today's turbulent environment, organizations, including those in the energy sector, need to build organizational resilience. Nevertheless, the nature of the relationship between digital transformation and organizational resilience has not yet been sufficiently clarified. Focusing on the level of digital transformation, and more precisely within the two dimensions of digital maturity, i.e. digital intensity and transformation management intensity, as well as based on the perspective of dynamic capabilities, this study developed a configurational framework and proposed a theoretical model to study the equifinal paths through which digital transformation and dynamic capabilities influence organizational resilience in energy sector companies. Based on a fuzzy set qualitative comparative analysis (fs/QCA) conducted on selected companies in the energy sector, i.e. Polish CHP plants, the relationship between digital transformation, dynamic capabilities and organizational resilience was investigated. The results show that a high level of organizational resilience can be achieved through two main paths based on the dominance of dynamic capabilities and the dominance of digital maturity. The study found that digital maturity can significantly influence CHP resilience. Moreover, the transformation management intensity is strongly related to high organizational resilience. The paper concludes by describing theoretical and practical implications, as well as research limitations and prospects for future research.

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

In fuzzy decision problems, the ordering of fuzzy numbers is the basic problem. Among which, the fuzzy preference relation is the reasonable one to represent preference relation by a fuzzy membership function. This paper studies the Nakamura’s and Kołodziejczyk’s preference relations. Eight cases of representing different level of overlapping between two triangular fuzzy numbers are considered. We analyze the ranking behaviors of all possible combinations of decomposition and intersection of two fuzzy numbers for the Nakamura’s and Kołodziejczyk’s preference relations of these test cases. The results indicate that the decomposition and intersection can affect the fuzzy preference relations, thereby the final total order relation of fuzzy numbers.

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprised of fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed wing aircraft systems. Here the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity techniquesto recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models will enable us to avoid common control design methods, such as gain scheduling, where stability issues can be extremely challenging.

We present a new unsupervised method aimed to obtain a partition of a complex urban system in homogenous urban areas, called urban contexts. The area of study is initially partitioned in microzones, homogeneous portion of the urban system, that are the atomic reference elements for the census data. With the contribution of domain experts, we identify the physical, morphological, environmental and socio-economic indicators need to identify synthetic characteristics of urban contexts and create the fuzzy rule set necessary to determine the type of urban context. We implement the set of spatial analysis processes necessary to calculate the indicators for microzone and apply a Mamdani fuzzy rule system to classify the microzones. Finally, the partition of the area of study in urban contexts is obtained by dissolving continuous microzones belonging to the same type of urban context. Tests are performed on the Municipality of Pozzuoli (Naples - Italy); the reliability of out model is measured by comparing the results with the ones obtained by detailed analysis.

In this study, the fuzzy c- means classifier has been studied with nine other similarity and dissimilarity measures: Manhattan distance, chessboard distance, Bray-Curtis distance, Canberra, Cosine distance, correlation distance, mean absolute difference, median absolute difference and normalised squared Euclidean distance. Both single and composite modes were used with a varying weight constant (m) and also at different α-cuts. The two best single norms obtained were combined to study the effect of composite norms on the datasets used. An image to image accuracy check was conducted to assess the accuracy of the classified images. Fuzzy Error Matrix (FERM) was applied to measure the accuracy assessment outcomes for a Landsat-8 dataset with respect to the Formosat-2 dataset. To conclude FCM classifier with Cosine norm performed better than the conventional Euclidean norm. But, due to the incapability of the FCM classifier to handle noise properly, the classification accuracy was around 75%.

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

The article outlines a creative approach by fusing ideas from fuzzy contractions, graph mappings, and Kannan mappings to create a brand-new notion known as "Kannan-graph-fuzzy contraction." This combination of concepts makes it possible to create a unique framework for resolving real-world issues controlled by nonlinear models. It is anticipated that using Kannan-graph-fuzzy contractions will offer a fresh approach to discussing solution existence in situations where these ideas overlap. This strategy might have a significant impact on a lot of real-world applications, proving how practical multidisciplinary techniques are for tackling issues in the real world originating from technology and engineering. The article includes several illustrated examples based on computer simulations, making the results more explicit.

Rapid Visual Screening (RVS) is a procedure that estimates structural scores for buildings and prioritize their retrofit and upgrade requirements. Despite the speed and simplicity of RVS, many of the collected parameters are non-commensurable and include subjectivity due to visual observations. It might cause uncertainties in the evaluation, which emphasizes the use of a fuzzy-based method. This study aims to propose a novel RVS methodology based on the interval type-2 fuzzy logic system (IT2FLS) to set the priority of vulnerable building to undergo detailed assessment while covering uncertainties and minimizing their effects during evaluation. The proposed method estimates the vulnerability of a building, in terms of Visual Damage Index, considering the number of stories, age of building, plan irregularity, vertical irregularity, building quality, and peak ground velocity, as inputs with a single output variable. Applicability of the proposed method has been investigated using a post-earthquake damage database of 28 reinforced concrete buildings from the Bingöl earthquake in Turkey.

The paper proposes TOPSIS method for solving multi-objective multi-level programming problem (MO-MLPP) with fuzzy parameters via fuzzy goal programming (FGP). At first, - cut method is used to transform the fuzzily described MO-MLPP into deterministic MO-MLPP. Then, for specific , we construct the membership functions of distance functions from positive ideal solution (PIS) and negative ideal solution (NIS) of all level decision makers (DMs). Thereafter, FGP based multi-objective decision model is established for each level DM for obtaining individual optimal solution. A possible relaxation on decisions for all DMs is taken into account for satisfactory solution. Subsequently, two FGP models are developed and compromise optimal solutions are found by minimizing the sum of negative deviational variables. To recognize the better compromise optimal solution, the concept of distance functions is utilized. Finally, a novel algorithm for MO-MLPP involving fuzzy parameters is provided and an illustrative example is solved to verify the proposed procedure.

As a new approach, for a nonzero normed algebra $A$, we will define some different classes of algebra fuzzy norms on $A$ generated by homomorphisms and continuous homomorphisms. Also as a source of examples and counterexamples in the field of fuzzy normed algebras, separate continuity of the elements of each class are investigated.

Contract violations, uncontracted load, and the alternating nature of electricity are the key causes of the frequency irregularity and Unscheduled Interchange (UI) / Deviation Settlement pricing in a restructured organized smart grid. These variations cause the frequency to fluctuate. The topic of frequency variation is discussed in this paper under various market circumstances. To correct frequency discrepancies under various market conditions, a fleet of electrical vehicles (EV) is offered as a distributed energy storage (DES). A bidirectional charger with a PI controller is suggested for the EV bidirectional power transfer. It is suggested to use a fuzzy logic (FL) controller to modify the proportional-integral (PI) controller gains. It has been noted that utilizing such a new approach lowers the UI prices.

This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: the two disjoint union fuzzy sets, the two disjoint fuzzy sets and the two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for the two disjoint union fuzzy sets. There are 42 candidate representations of a comparison measure for the two disjoint fuzzy sets. Of which 13 candidate representations with one or two terms can be used to easily calculate and compare a comparison measure.

In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the partition requirement, that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measuring terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy.

The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e. stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T–S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T–S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

Resource conflicts represent a significant global challenge in regions abundant with natural re-sources. Modelling the myriad factors driving natural resource-based conflicts (NRBCs), spanning environmental, health, socio-economic, and political dimensions, is a complex endeavor exacer-bated by data scarcity. Furthermore, existing quantitative studies often focus solely on large-scale conflicts. This article introduces a novel algorithm, the Spatially Explicit Fuzzy Logic-Adapted Model for Conflict Management (SEFLAME-CM), which integrates the local knowledge of stakeholders into spatial decision-making technologies to support sustainable peace efforts. The results are validated with spatial multi-criteria evaluation (SMCE) using spatial statistics. The Moran’s I scatter plots for the overall conflicts reveal significant values of 0.99 and 0.98 for both the SEFLAME-CM and SMCE, respectively, with significant spatial autocorrelation. While there re-mains room for improvement in enhancing the model's quality, SEFLAME-CM demonstrates its capacity to transparently model complex real-world problems. The findings underscore the im-perative for a holistic approach to addressing environmental degradation, socio-economic, and political drivers of resource conflicts at the community level. Our paper demonstrates the signif-icance of spatial information technologies and knowledge exchange between experts and local stakeholders in effectively managing resource conflicts. These insights should inform national policies and international interventions, ensuring that the complex underlying issues are ad-dressed while prioritizing the knowledge and needs of affected communities.

Abstract—The static and fatigue analysis of plates with holes, made of 2D woven roving composites, is conducted. The parametrization of convex holes is proposed. Experimental results of specimens without holes and with different shapes of notches are discussed. The fatigue behaviour is considered with the use of the low cycle fatigue method. The analysis is supplemented by the numerical finite element modeling. The present work is an extension of the results discussed in the literature. The finite element modeling of plates with holes is presented in details in Ref [1-3] including also the problems of the accuracy. The experimental results and the form of specimens are shown in Ref [4]. Two parametrical description of static and fatigue behaviour of plates with holes characterizes the goal and the novelty of the paper. The fuzzy approach is employed to reduce the number of experimental data [5].

Background: With the rapid improvement of the healthcare technologies, security and privacy of the most sensitive data, health data is at risk. Protecting patient privacy has many components, even though the data are in electronic format. Although patient privacy is thoroughly discussed in the literature, there is no study presenting all components of patient privacy protection. Methods: In this study, a complete evaluation framework is presented, as an evaluation tool, an inventory is developed, reliability and validity of the inventory is examined. Study is conducted in three phases: Conceptual framework development, inventory development and an evaluation case study. In the evaluation, fuzzy conjoint analysis is employed to handle the subjectivity and am-biguity. As the result of the evaluation, the institution is given a patient privacy protection ma-turity grade, between 1 and 5, where 1 is the worst and 5 is the best grade. Results: In the case study, XXX’s biggest hospital, employing 800 nurses, is evaluated. Half of the nurses, 400, have partici-pated in the study. Literature tells healthcare institutions do not invest enough to protect patient privacy, and the study results support this finding. Institution’s maturity grade resulted as level 2, which is bad. Conclusion: The study measures he privacy maturity with many evaluation com-ponents. Result of the evaluation explains to the patients and the public if their data is safe or not. With this maturity grade, patients have an idea about which institution to choose, public can conclude the institutions’ reliability in terms of patient privacy.

The growing importance of sustainability in organizational success, particularly in the pharma-ceutical industry, underscores the need for leveraging technologies like blockchain to enhance sustainability indicators across environmental, social, and economic pillars. This study aims to identify and understand the challenges hindering the adoption of blockchain in the pharmaceuti-cal sector for improving sustainability performance, addressing two research questions: the spe-cific challenges faced by blockchain adoption in this context and the interdependencies among these challenges. Employing a two-step approach, the study compiles challenges through a litera-ture review, refines them via expert opinions, and establishes their interrelationships using methodologies like Fuzzy Interpretive Structural Modeling (FISM) and Cross-Impact Matrix Multiplication Applied to Classification (MICMAC). The research contributes to unraveling the complex relationships and dependencies within the system, providing a structured framework for improved decision-making and strategic planning. It fills a literature gap by being the first attempt to outline driving and dependent factors related to the challenges of adopting blockchain technology for sustainability enhancement in the pharmaceutical sector, offering insights that can significantly impact brand image, company perception, and consumer value.

This paper will present the torque control design of an AFPMSM, one stator, and one rotor, using an FLC and ANFIS in-wheels fed by a three-level T-type inverter. The Surgeon ambiguous inference file of the FLC controller is built by two input vectors, the stator current error and the derivative of the stator error. These input variables include five membership functions, Negative big (NB), Negative small (NS), Equal zero (ZE), Positive small (PS), and Positive big (PB). The FLC controller is implemented with a 5x5 matrix so that the output stator voltage of the controller is required. The ANFIS controller for the neural network-based feature set and the fuzzy system. The neural network develops the dataset on the stator current error (e) and error integral (∆e). Then, the generated dataset is fed to the fuzzy logic method, and the control rules are developed. This ANFIS controller is caused by the training and testing phases. Finally, the FLC and ANFIS torque controllers are compared with the PI controller. The correctness of the proposed control structured solution is demonstrated by the simulation results of MATLAB/SIMULINK.

Coagulation is the most sensitive step in drinking water treatment. Underdosing may not yield the required water quality, whereas overdosing may result in higher costs and excess sludge. Traditionally, the coagulant dosage is set based on bath experiments performed manually. Therefore, this test does not allow real-time dosing control, and its accuracy is subject to operator experience. Alternatively, solutions based on machine-learning (ML) have been evaluated as a computer-aided alternative. Despite these advances, there is open debate on the most suitable ML method applied to the coagulation process, capable of the most highly accurate prediction. This study addresses this gap, where a comparative analysis between ML methods was performed. As a research hypothesis, a novel data-driven fuzzy inference system (FIS) should provide the best performance due to its ability to deal with uncertainties inherent to complex processes. Although ML methods have been widely investigated, only a few studies report hybrid neuro-fuzzy systems applied to coagulation. Thus, to the best of our knowledge, this is the first study thus far to address the accuracy of this novel data-driven FIS for such application. The novel FIS provided the smallest error (0.86), indicating a promising alternative tool for real-time and highly accurate coagulant dosing in drinking water treatment.

This study aims to elucidate a soft computing approach for quantitative assessment of the scoring grade or rubrics for students in an outcome based education system. The intended approach resorts to a fuzzy membership based assessment of the different parameters of the scoring system, thereby yielding a novel and humanly assessment technique. The selection of the membership functions is based on the human behavior so as to make a realistic representation of the scoring strategy. The novelty of the proposed strategy lies in assigning fuzzy membership based weighted scores instead of simply assigning score bands to rubric categories, as is performed in normal rubrics based assessment. Comparative results demonstrated on a case study of Indian education scenario reveal the effectiveness of the proposed strategy over other fuzzy membership and normal rubrics based assessment procedures.

More than 110 countries including 500 cities worldwide have set the goal of reaching carbon neutrality. Heating contributes to most of the residential energy consumption and carbon emissions. The green energy transition of fossil-based heating systems is needed to reach the emission goals. However, the heating systems vary in energy source, heating technology, equipment location, and these complexities make it challenging for households to compare heating systems and make decisions. Hence, a decision support tool that provides a generalized ranking of individual heating alternatives is proposed for households as decision-makers to identify the optimal choice. This paper presents an analysis of 13 heating alternatives and 19 quantitative criteria in technological, environmental, and financial aspects, combines ideal solution based Multi-Criteria Decision Making with 6 weighting methods and 4 normalization methods, and introduces ensemble learning with a fuzzy membership function derived from Cauchy distribution to finalize the final ranking. The robustness of the proposed method is verified by 3 sensitive analyses from different aspects. Air to water heat pump, solar heating and direct district heating are the top three rankings in the final result under Danish national average data. A framework is designed to guide the decision-makers apply this ranking guideline with their practical feasible situations.