This paper presents an unsupervised feature selection method for multi-dimensional histogram-valued data. We define a multi-role measure, called the compactness, based on the concept size of given objects and/or clusters described by a fixed number of equal probability bin-rectangles. In each step of clustering, we agglomerate objects and/or clusters so as to minimize the compactness for the generated cluster. This means that the compactness plays the role of a similarity measure between objects and/or clusters to be merged. To minimize the compactness is equivalent to maximize the dis-similarity of the generated cluster, i.e., concept, against the whole concept in each step. In this sense, the compactness plays the role of cluster quality. We also show that the average compactness of each feature with respect to objects and/or clusters in several clustering steps is useful as feature effectiveness criterion. Features having small average compactness are mutually covariate, and are able to detect geometrically thin structure embedded in the given multi-dimensional histogram-valued data. We obtain thorough understandings of the given data by the visualization using dendrograms and scatter diagrams with respect to the selected informative features. We illustrate the effectiveness of the proposed method by using an artificial data set and real histogram-valued data sets.

In this essay, the new notion concerning longest path is introduced. Longest path has a close relation with the notion of diameter in graph. The classes of graph are studied in the terms of having the vertex with longest path. Valued number is the number of edges belong to the longest path in the matter of vertex. For every vertex, there’s a valued number and new notion of valued set is the generalization of valued number for the vertex when all vertices of the graphs are corresponded to a vertex which has the greater valued number. For any positive integer, there’s one graph in that, there’s vertex which its valued number is that. By deleting the vertices which don’t belong to valued set, new notion of new graph is up. It’s called valued graph. The comparison amid valued graph and initial graph is up, too.

The aim of this article is to introduce the new notion on a given graph. The notions of valued set, valued function, valued graph and valued quotient are introduced. The attributes of these new notions are studied. Valued set is about the set of vertices which have the maximum number of neighbors. The kind of partition of the vertex set to the vertices of the valued set is introduced and its attributes are studied. The behaviors of classes of graphs under these new notions are studied and the algebraic operations on these sets in the different situations get new result to understand the classes of graphs, these notions and the general graphs better and more.

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.

Deepfakes are manipulated or altered images, or video, that are created using deep learning models with high levels of photorealism. The two popular methods of producing a deepfake are based on either convolutional neural networks (CNN), or autoencoders. Deepfakes created using CNN comparatively show higher qualities of realism, yet oftentimes leave artifacts and distortions in the generated media that can be detected using machine learning and deep learning algorithms. In recent years, there has been an influx of periocular image and video data because of the increase usage of face masks. By wearing masks, much of what is used for facial recognition is hidden, leaving only the periocular region visible to an observer. This loss of vital information leads to easier misidentification of media, allowing deepfakes to less likely be identified as fake. In this work, feature extraction methods, such as Scale-Invariant Feature Transform (SIFT), Histogram of Oriented Gradients (HOG), and CNN, are used to train an ensemble deep learning model to detect deepfakes in videos on a frame-by-frame level based on the periocular region. Our proposed model is able to distinguish original and manipulated images with accuracies around 98.9 percent, which is an improvement to previous works by combining SIFT and HOG for deepfake detection in convolutional neural networks.

It is increasingly common for experiments in biology and medicine to involve large numbers of hypothesis tests. A natural graphical method for visualizing these tests is to construct a histogram from the p-values of these tests. In this article, we examine the shapes, both normal and abnormal, that these histograms can take on, as well as present simple inferential procedures that help to interpret the shapes in terms of diagnosing potential problems with the experiment. We examine potential causes of these problems in detail, and discuss potential remedies. Throughout, examples of abnormal-looking p-value histograms are provided and based on case studies involving real biological experiments.

This paper has two major parts. In the first part histogram equalization for the image enhancement was implemented without using the built-in function in MATLAB. Here, at first, a color image of a rat was chosen and the image was transformed into a grayscale image. After this conversion, histogram equalization was implemented on the grayscale image. Later on, in the same image for each RGB channel, histogram equalization was implemented to observe the effect of histogram equalization on each channel. In the end, the histogram equalization was implemented to this specific color image of a rat. In the second part, for the grayscale image in part 1, the desired histogram of another colored image of a rat was introduced and histogram specification was implemented on the original colored image.

This paper has two major parts. In the first part histogram equalization for the image enhancement was implemented without using the built-in function in MATLAB. Here, at first, a color image of a rat was chosen and the image was transformed into a grayscale image. After this conversion, histogram equalization was implemented on the grayscale image. Later on, in the same image for each RGB channel, histogram equalization was implemented to observe the effect of histogram equalization on each channel. In the end, the histogram equalization was implemented to this specific color image of a rat. In the second part, for the grayscale image in part 1, the desired histogram of another colored image of a rat was introduced and histogram specification was implemented on the original colored image.

In this article, we show the existence of fixed point for the derivative of interval-valued functions. Meanwhile, the fixed point inquiry will utilize the common fixed point methods under the condition of compatibility of the hybrid composite mappings in the sense of the Hausdorff metric. Some examples are given to support the usability of the result of this research .

In recent decades, power consumption has become an essential factor in attracting the attention of integrated circuit (IC) designers. Multiple-valued logic (MVL) and approximate computing are some techniques that could be applied to integrated circuits to make power-efficient systems. By utilizing MVL-based circuits instead of binary logic, the information conveyed by digital signals increases, and this reduces the required interconnections and power consumption. On the other hand, approximate computing is a class of arithmetic computing used in systems where the accuracy of the computation can be traded-off for lower energy consumption. In this paper, we propose novel designs for exact and inexact ternary multipliers based on carbon-nanotube field-effect transistors (CNFETs). The unique characteristics of CNFETs make them a desirable alternative to MOSFETs. The simulations are conducted using Synopsys HSPICE. The proposed design is compared against existing ternary multipliers. The results show that the proposed exact multiplier reduces energy consumption by up to 6X. At the same time, the best inexact design improves energy efficiency by up to 35X compared to the latest state-of-the-art methods. Using the imprecise multipliers for image processing provides evidence that these proposed designs are a low-power system with an acceptable error.

The hard-shelled seed industry plays an important role in the global agricultural economy. As a result of nut industrialization, considerable amounts of by-products and residues are produced year by year, burnt as fuel or discarded as non-valued waste, by-passing a potential source of valuable compounds or features. Over the last decade nutshells have received great interest due to their lignin concentration and their antioxidant, physical and mechanical features. It was found that these properties vary among cultivars, latitude and localities of plantation. On the other hand, there is inconsistences regarding to mechanical and some biochemical properties of both nutshells, which aimed to explore the status of potential hazelnut and walnut shells appli-cations into sustainable circular bio-economy chains. Hence, this review deals with the recent scientific literature on their chemical composition as well as their functional applications as an approach to sustain the utilization of the main by-product derived from the nut-industry.

Due to the advantages of low latency, low power consumption and high flexibility of FPGA-based acceleration technology, it has been more and more widely studied and applied in the field of computer vision in recent years. An FPGA-based feature extraction and tracking accelerator for real-time visual odometry (VO) and visual simultaneous localization and mapping (V-SLAM) is proposed, which can realize the complete acceleration processing capability of the image front-end and directly output the feature point ID and coordinates to the backend. The accelerator consists of image preprocessing, pyramid processing, optical flow processing, and feature extraction and tracking modules. For the first time, it implements a hardware solution that combines features from accelerated segment test (FAST) corners with Gunnar Farneback (GF) dense optical flow, to achieve better feature tracking performance and provide more flexible technical route selection. In order to solve the scale invariance and rotation invariance lacking problem of FAST features, an efficient pyramid module with a five-layer thumbnail structure is designed and implemented. The accelerator is implemented on a modern Xilinx Zynq FPGA. The evaluation result shows that the accelerator can achieve stable tracking of features of violently shaking images, and is consistent with the results of MATLAB code running on PC. When operating at 100MHz, the accelerator can process 108 frames per second for 720P images and 48 frames per second for 1080P images. Compared to PC CPUs that consume seconds of time, the processing latency is greatly reduced to the order of milliseconds, making GF dense optical flow an efficient and practical technical solution on the edge side.

Ancient numismatics, that is, the study of ancient currencies (predominantly coins), is an interesting domain for the application of computer vision and machine learning, and has been receiving an increasing amount of attention in recent years. Notwithstanding the number of articles published on the topic, the variety of different methodological approaches described, and the mounting realisation that the relevant problems in the field are most challenging indeed, all research to date has entirely ignored one specific, readily accessible modality: colour. Invariably, colour is discarded and images of coins treated as being greyscale. The present article is the first one to question this decision (and indeed, it is a decision). We discuss the reasons behind the said choice, present a case why it ought to be reexamined, and in turn investigate the issue for the first time in the published literature. Specifically, we propose two new colour-based representations specifically designed with the aim of being applied to ancient coin analysis, and argue why it is sensible to employ them in the first stages of the classification process as a means of drastically reducing the initially enormous number of classes involved in type matching ancient coins (tens of thousands, just for Ancient Roman Imperial coins). Furthermore, we introduce a new data set collected with the specific aim of denomination-based categorisation of ancient coins, where we hypothesised colour could be of potential use, and evaluate the proposed representations. Lastly, we report surprisingly successful performances which goes further than confirming our hypothesis—rather, they convincingly demonstrate a much higher relevant information content carried by colour than even we expected. Thus we trust that our findings will be noted by others in the field and that more attention and further research will be devoted to the use of colour in automatic ancient coin analysis.

We propose a novel method for salient object detection in different images. Our method integrates spatial features for efficient and robust representation to capture meaningful information about the salient objects. We then train a conditional random field (CRF) using the integrated features. The trained CRF model is then used to detect salient objects during the online testing stage. We perform experiments on two standard datasets and compare the performance of our method with different reference methods. Our experiments show that our method outperforms the compared methods in terms of precision, recall, and F-Measure.

In this paper, the author obtains an analytic exact form of Heaviside function, which is also known as Unit Step function and constitutes a fundamental concept of the Operational Calculus.In particulat, this function is explicitly expressed in a very simple manner by the aid of purely algebraic representations. The novelty of this work is that the proposed explicit formula is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Hence, it may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

This paper is devoted to the study of reproducing kernels on 2-inner product Hilbert spaces. We focus on a new structure to produce reproducing kernel Hilbert and Banach spaces. According to multi-variable computing, this structures can be useful in electrocardiographs, machine learning and economy

Accurate medical image segmentation is paramount for precise diagnosis and treatment in modern healthcare. This research presents a comprehensive study on the efficacy of Particle Swarm Optimization (PSO) combined with Histogram Equalization (HE) preprocessing for medical image segmentation, focusing on Lung CT-Scan and Chest X-ray datasets. Best Cost values reveal the PSO algorithm’s performance, with HE preprocessing demonstrating significant stabilization and enhanced convergence, particularly in complex Lung CT-Scan images. Evaluation metrics, including Accuracy, Precision, Recall, F-Score, Specificity, Dice, and Jaccard, show substantial improvements with HE preprocessing, emphasizing its impact on segmentation accuracy. Comparative analyses against alternative methods, such as Otsu, Watershed, and K-means, confirm the competitiveness of the PSO-HE approach, especially in Chest X-ray images. The study also underscores the positive influence of preprocessing on image clarity and precision. These findings highlight the promise of the PSO-HE approach in advancing the accuracy and reliability of medical image segmentation, paving the way for further research and method integration to enhance this critical healthcare application.

The IoT Internet of Things being a promising technology of the future. It is expected to connect billions of devices. The increased communication number is expected to generate data mountain and the data security can be a threat. The devices in the architecture are fundamentally smaller in size and low powered. In general, classical encryption algorithms are computationally expensive and this due to their complexity and needs numerous rounds for encrypting, basically wasting the constrained energy of the gadgets. Less complex algorithm, though, may compromise the desired integrity. In this paper we apply a lightweight encryption algorithm named as Secure IoT (SIT) to a quantized speech image for Secure IoT. It is a 64-bit block cipher and requires 64-bit key to encrypt the data. This quantized speech image is constructed by first quantizing a speech signal and then splitting the quantized signal into frames. Then each of these frames is transposed for obtaining the different columns of this quantized speech image. Simulations result shows the algorithm provides substantial security in just five encryption rounds.

In this paper, a positive answer to the open question of Fabino et al. is given, and the concept of I\c sik type set valued contractions is introduced and fixed point theorem for such contractions is established. Examples to support main theorems are given, and an application to integral inclusion is given.

In this paper, we shall introduce the interval-valued spatial error model. Based on the idea of least square method of single-valued case, we give the parameter estimator for interval-valued spatial error model. The theoretical properties of the proposed estimator are proved. Finally, we give the numerical analysis and a real example.

Facial Emotion Recognition (FER) is crucial across psychology, neuroscience, computer vision, and machine learning due to the diversified and subjective nature of emotions, varying considerably across individuals, cultures, and contexts. This paper investigates the impact of histogram equalization, data augmentation and model optimization strategies on three well-known FER datasets using pre-trained VGG models. Additionally, this paper showcases the effectiveness of different regularization techniques, callbacks, and learning schedulers in enhancing model performance by conducting extensive experiments. The model evaluation is discussed in terms of the following metrics: Accuracy, Area Under the Receiver Operating Characteristic Curve (AUC-ROC), Area Under the Precision-Recall Curve (AUC-PRC), and Weighted F1 score. Notably, the fine-tuned VGG models exhibit state-of-the-art performance compared to more complex conventional transfer learning models resulting in accuracies of 100%, 95.92%, and 69.65% on the CK+, KDEF, and FER2013 datasets, respectively.

This paper aims to implement histogram pyramids with marching cubes method for 3D medical volumetric rendering. The histogram pyramids are used for feature extraction by segmenting the image into the hierarchical order like the pyramid shape. The histogram pyramids can decrease the number of sparse matrixes that will occur during voxel manipulation. The important feature of the histogram pyramids is the direction of segments in the image. This feature will be then used for connecting pixels (2D) to form up voxel (3D) during marching cubes implementation. The proposed method is fast and easy to implement and it also produces a smooth result (compared to the traditional marching cubes technique). The experimental results show that time consuming for generating 3D model can be reduced by 15.59% in average. The paper also shows the comparison between the surface rendering using the traditional marching cubes and the marching cubes with histogram pyramids. Therefore, for the volumetric rendering such as 3D medical models and terrains where a large number of lookups in 3D grids are performed, this method is a particularly good choice for generating the smooth surface of 3D object.

This proposed research explores a novel approach to image classification by deploying a complex-valued neural network (CVNN) on a field-programmable gate array (FPGA), specifically for classifying 2D images transformed into polar form. The aim of this research is to address the limitations of existing neural network models in terms of energy and resource efficiency, by exploring the potential of FPGA-based hardware acceleration in conjunction with advanced neural network architectures like CVNNs. The methodological innovation of this research lies in the Cartesian to polar transformation of 2D images, effectively reducing the input data volume required for neural network processing. Subsequent efforts focused on constructing a CVNN model optimized for FPGA implementation, emphasizing the enhancement of computational efficiency and overall performance. The experimental findings provide empirical evidence supporting the efficacy of the image classification system developed in this study. One of the developed models, CVNN_128, achieves an accuracy of 88.3% with an inference time of just 1.6ms and a power consumption of 4.66mW for the classification of the MNIST test dataset consists of 10,000 frames. While there is a slight concession in accuracy compared to recent FPGA implementations that achieve 94.43%, our model significantly excels in classification speed and power efficiency—surpassing existing models by more than a factor of 100. In conclusion, the paper demonstrates the substantial advantages of FPGA-implementation of CVNNs for image classification tasks, particularly in scenarios where speed, resource, and power consumption are critical. The study’s reproducible results and corresponding code are available on GitHub at the following link: https://github.com/mahmad2005/CVNNonFPGA

In the era of sustainable development, green supplier selection has become a key component of supply chain management, as it considers criteria such as carbon footprint, water usage, energy usage and recycling capacity. Since the green supplier selection problem involves subjective criteria and uncertainty in preferences, it is well suited to using multi-criteria decision-making methods (MCDM). Although few researchers have investigated MCDM for green supplier selection under uncertainty using intuitionistic and Pythagorean fuzzy sets. Still, the newly developed fermatean fuzzy can handle greater data uncertainty than intuitionistic and Pythagorean fuzzy sets. Since interval extension of fuzzy theory provides more accurate modeling, in this paper, we propose an interval extension of fermatean fuzzy set and discuss its fundamental set operations, arithmetic operations and related properties. We propose the Hamming distance function and the score function of the interval-valued fermatean fuzzy numbers. The recently developed Multi-attribute Border Approximation Area Comparison (MABAC) method is also considered due to its stable and simple computation compared to other conventional MCDM methods. Therefore, an interval-valued fermatean fuzzy MABAC method is proposed and solved to select a green supplier based on multiple criteria. The proposed method's comparative analysis and sensitivity analysis validate the proposed method's effectiveness and robustness.

Extreme overvalued beliefs (EOB) are rigidly-held, shared beliefs that are the motive behind most acts of terrorism and mass shootings. EOBs are differentiated from delusions and obsessions. The concept of overvalued idea was first described by Wernicke and later applied to terrorism by McHugh. Our group of forensic psychiatrists (Rahman, Resnick, Harry) refined the definition as an aid in the differential diagnosis seen in acts of violence. The form and content of EOBs is discussed as well as group effects, conformity and obedience to authority. Religious cults such as: The People’s Temple, Heaven’s Gate, Aum Shinrikyo, Islamic State (ISIS) and conspiracy beliefs such as assassinations, moon-hoax and vaccine-induced autism beliefs are discussed using this construct. Finally, some concluding thoughts on countering violent extremism, including its online presence is discussed utilizing information learned from online eating disorder and consumer experience.

The Thailand automotive industry grapples with complex challenges in service parts management, demanding a strategic approach for post-sales operations. This research unveils a tailored methodology, leveraging historical sales data, refined part classifications, and strategic decision rules. A high-level overview of the automotive supply chain emphasizes interconnected stakeholders. The systematic methodology delves into part categorization, decision rules, and data analysis. Decision rule outcomes, exceptions, and contingency solutions showcase efficacy. A cost impact assessment highlights substantial savings. Visualization tools offer nuanced perspectives. Optimized service parts classification, robust stocking decision rules, and cost-effective strategies emerge. Support Vector Regression excels in forecasting, with recommendations for dynamic stocking. Implications extend to the broader industry, offering efficiency and service quality blueprints. Acknowledging limitations and suggesting future research, this study contributes a valuable framework for Thai automotive service parts management.

Along with the economic growth, the companies must contribute to social progress and promote environmental sustainability in equal harmony. Sustainable human resource management (SHRM) strategies make it possible to attain the economic, social and environmental goals of a firm. In this regard, a survey method is discussed using the literature review and online questionnaire to identify the main factors/indicators during the SHRM evaluation of manufacturing firms in India. Uncertainty is commonly occurred in the assessment of SHRM factors. As a generalized version of fuzzy sets, single-valued neutrosophic set (SVNS) has been demonstrated as a valuable tool to illustrate the indeterminate, inconsistent and uncertain data of realistic decision-making problems. Considering the idea of SVNSs, this study develops a hybrid multi-criteria group decision-making (MCGDM) approach for assessing the SHRM of manufacturing firms under uncertainty settings. For this purpose, an SVN-alternative ranking order method accounting for two-step normalization (AROMAN) is proposed based on VIFI-score function-based decision experts’ (DEs’) weighting tool and integrated criteria weight-determining model to solve the MCGDM problems with fully unknown DEs and criteria weights. In this regard, we develop new SVN-distance measure to compute the degree of difference between SVNSs. Some examples are presented to demonstrate the efficacy of developed measure over the existing ones. In addition, new criteria weight-determination model is presented with the integration of objective weights through IVIF-distance measure-based model and subjective weights through ranking comparison (RANCOM) tool on SVNSs. The proposed ranking method is applied to an empirical study of SHRM assessment for manufacturing firms in India, which shows its applicability and feasibility. In this study, the evaluation criteria are characterized into social, environmental and economic aspects with DE’s opinions. Comparative and sensitivity analyses are made to show the strength and steadiness of presented approach. This study provides an innovative MCGDM analysis framework, which makes a significant contribution to the SHRM assessment problem under indeterminate, inconsistent and uncertain setting.

Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying \begin{align*} \left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2, \quad \forall \lambda_j \in \mathbb{K}, 1\leq j \leq n, \forall n \in \mathbb{N}. \end{align*} For $d\in \mathbb{N}$, let $\mathbb{K}^d$ be the standard $d$-dimensional non-Archimedean Hilbert space. Let $m \in \mathbb{N}$ and $\text{Sym}^m(\mathbb{K}^d)$ be the non-Archimedean Hilbert space of symmetric m-tensors. We prove the following result. If $\{\tau_j\}_{j=1}^n$ is a collection in $\mathbb{K}^d$ satisfying $\langle \tau_j, \tau_j\rangle =1$ for all $1\leq j \leq n$ and the operator $\text{Sym}^m(\mathbb{K}^d)\ni x \mapsto \sum_{j=1}^n\langle x, \tau_j^{\otimes m}\rangle \tau_j^{\otimes m} \in \text{Sym}^m(\mathbb{K}^d)$ is diagonalizable, then \begin{align}\label{WELCHNONABSTRACT} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |\langle \tau_j, \tau_k\rangle|^{2m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{WELCHNONABSTRACT}) as the non-Archimedean version of Welch bounds obtained by Welch [\textit{IEEE Transactions on Information Theory, 1974}]. We formulate non-Archimedean Zauner conjecture.

In this paper, we classify the function space of all real-valued functions on R denoted as F(R,R) into 28 distinct blocks. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection, which reveals a special relationship structure between four well-known real-valued functions in real analysis: the Cantor function, Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored.

Traditional silicon binary circuits continue to face challenges such as high leakage power dissipation and large area of interconnections. Multiple-Valued Logic (MVL) and nano-devices are two feasible solutions to overcome these problems. In this paper, we present a novel method to design ternary logic circuits based on Carbon Nanotube Field Effect Transistors (CNFETs). The proposed designs use the unique properties of CNFETs, e.g., adjusting the Carbon Nanotube (CNT) diameters to have the desired threshold voltage and have the same mobility of P-FET and N-FET transistors. Each of our designed logic circuits implements a logic function and its complementary via a control signal. Also, these circuits have a high impedance state which saves power while the circuits are not in use. We show a more detailed application of our approach by designing a two-digit adder-subtractor circuit. We simulate the proposed ternary circuits using HSPICE via standard 32nm CNFET technology. The simulation results indicate the correct operation of the designs under different process, voltage and temperature (PVT) variations. Moreover, we designed a two-digit adder/subtractor and a power efficient ternary logic ALU based on the proposed gates. Simulation results show that the two-digit adder/subtractor using our proposed gates has 12X and 5X lower power consumption and PDP (power delay product) respectively, compared to previous designs.

The vast majority of autonomous driving systems are limited to applications on roads with clear lane markings and are implemented using commercial grade sensing systems coupled with specialized graphic accelerator hardware. This research reviews an alternative approach for autonomously steering vehicles that eliminates the dependency on road markings and specialized hardware. A combination of machine vision, machine learning and artificial intelligence based on popular pre-trained Convolutional Neural Networks (CNN) and Recurrent Neural Networks (RNN) was used to drive a vehicle along roads lacking lane markings (unmarked roads). The team developed and tested this approach on the ACTor (Autonomous Camus TranspORt) vehicle - an autonomous vehicle development and research platform coupled with a low-cost webcam based sensing system and minimal computational resources. The proposed solution was evaluated on real-world roads and varying environmental conditions. It was found that this solution may be used to successfully navigate unmarked roads autonomously with acceptable road following behavior.

Surface water distribution extracted from remote sensing data has been used in water resource assessment, coastal management, and environmental change studies. Traditional manual methods for extracting water bodies cannot satisfy the requirements for mass processing of remote sensing data; therefore, accurate automated extraction of such water bodies has remained a challenge. The histogram bimodal method (HBM) is a frequently used objective tool for threshold selection in image segmentation. The threshold is determined by seeking twin peaks, and the valley values between them; however, automatically calculating the threshold is difficult because complex surfaces and image noise which lead to not perfect twin peaks (single or multiple peaks). We developed an operational automated water extraction method, the modified histogram bimodal method (MHBM). The MHBM defines the threshold range of water extraction through mass static data; therefore, it does not require the identification of twin histogram peaks. It then seeks the minimum values in the threshold range to achieve automated threshold. We calibrated the MHBM for many lakes in China using Landsat 8 Operational Land Imager (OLI) images, for which the relative error (RE) and squared correlation coefficient (R2) for threshold accuracy were found to be 2.1% and 0.96, respectively. The RE and root-mean-square error (RMSE) for the area accuracy of MHBM were 0.59% and 7.4 km2. The results show that the MHBM could easily be applied to mass time-series remote sensing data to calculate water thresholds within water index images and successfully extract the spatial distribution of large water bodies automatically.

We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic Sz.-Nagy dilation for p-adic magic contraction.

Single valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single valued neutrosophic cross entropy bears an asymmetrical behavior and produce an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under single valued neutrosophic set (SVNS) environment namely SN- cross entropy and prove its basic properties. Also we define weighted SN-cross entropy measure and investigate its basic properties. We develop a new multi attribute group decision making (MAGDM) strategy for ranking of the alternatives based on the proposed weighted SN-cross entropy measure between each alternative and the ideal alternative. Finally, a numerical example of MAGDM problem of investment potential is solved to show the validity and efficiency of proposed decision making strategy. We also present comparative anslysis of the obtained result with the results obtained form the existing solution strategies in the solution.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexity, we establish necessary and sufficient optimality conditions for local strong quasi and approximate $LU$-efficient solutions to nonsmooth optimization problems with interval-valued multiobjective functions.

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

: On earth, plants play the most important part. Every organ of a plant plays a vital role in the ecological field as well as the medicinal field. But on the whole earth there are several species of plants are available. Different plants have different diseases. Therefore it is needed to identify the plants and their diseases to prevent loss. Now to identify the plants and their diseases manually is very time consuming. In this research an automatic plant and their disease detection system is proposed. For experimental purposes, high-quality leaf images are accepted for training and testing. For detecting the healthy and diseased area in a leaf, region-based and color-based region thresholding techniques were used. For feature selection Histogram Oriented Gradient (HOG) and Local Binary Pattern (LBP) method were applied. Finally for classification two-class and multi-class Support Vector Machine (SVM) was used. It is observed that both feature selection processes with SVM give 99% accuracy. Finally to understand the automated system a graphical user interface was created for all users.

The paper demonstrates the analysis of Corona Virus Disease based on a probabilistic model. It involves a technique for classification and prediction by recognizing typical and diagnostically most important CT images features relating to Corona Virus. The main contributions of the research include predicting the probability of recurrences in no recurrence (first time detection) cases at applying our proposed approach for feature extraction. The combination of the conventional statistical and machine learning tools is applied for feature extraction from CT images through four images filters in combination with proposed composite hybrid feature extraction (CHFS). The selected features were classified by the stack hybrid classification system(SHC). Experimental study with real data demonstrates the feasibility and potential of the proposed approach for the said cause.

Today, mobile phones are at the center of many consumers' lives and a part of people's lives. Although this tool was considered a luxury initially, it has gradually become a necessary tool with the reduction of the price and the increase of its functions. Consumers choose specific models of mobile phones according to their needs. Mobile phones have quality features that are expressed in the form of quality dimensions. These dimensions are mostly expressed by word of mouth (WOM). In this research, first; we collected the opinions of 350 students about 4 brands of mobile phones based on Garvin's quality of dimensions, finally; the students’ opinions about mobile phones were evaluated with integrated TOPSIS with interval-valued intuitionistic fuzzy numbers technique, and the priority of 4 phone brands was determined based on students' opinions.

The objective of the paper is to introduce new similarity measure for single valued neutrosophic sets based on logarithm function. We define logarithm similarity measure and their weighted similarity measure for single valued neutrosophic sets. Then we define hybrid logarithm similarity measure and weighted hybrid logarithm similarity measure for single valued neutrosophic sets. We prove the basic properties of the proposed measures. We then define an entropy function using logarithm function to determine unknown attribute weights. We develop a novel multi attribute group decision making strategy for single valued neutrosophic sets based on the weighted hybrid logarithm similarity measure. We address an illustrative example to demonstrate the effectiveness and aptness of the proposed strategies. We conduct a sensitivity analysis of the developed strategy. We also make a comparison between the obtained results from proposed strategies and different existing strategies in the literature.

Neutrosophic cubic set (NCS) is one of the important family members of neutrosophic hybrid sets. Neutrosophic cubic set has more strength than other family members of neutrosophic hybrid sets to express incomplete information due to the presence of interval valued neutrosophic set (IVNS) and single valued neutrosophic set (SVNS) in its structure. Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. In this paper we first define a new cross entropy measure under NCSs environment which we call NC- cross entropy measure. We investigate the basic properties of NC-cross entropy. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision making (MADM) strategy based on weighted NC-cross entropy. To show the feasibility and applicability, we solve a MADM problem using the proposed strategy.

Neutrosophic cubic set is the hybridization of the concept of neutrosophic set and interval neutrosophic set. Neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets appear in the current literature. In the present paper we propose the score, accuracy functions for neutrosophic cubic sets and prove their basic properties. We firstly develop TODIM method to solve multi attribute group decision making in neutrosophic cubic set environment, which we call NC-TODIM. Also, we solve a MAGDM problem using the proposed NC-TODIM method to show the applicability and effectiveness of the developed method. We also conduct sensitivity analysis to show the impact of ranking order of the alternatives for different values of attenuation factor of losses for multi-attribute group decision making problem.

Alzheimer's disease (AD) detection acting as an essential role in global health care due to misdiagnosis and sharing many clinical sets with other types of dementia, and costly monitoring the progression of the disease over time by magnetic reasoning imaging (MRI) with consideration of human error in manual reading. This paper goal a comparative study on the performance of data mining techniques on two datasets of Clinical and Neuroimaging Tests with AD. Our proposed model in the first stage, Apply clinical medical dataset to a composite hybrid feature selection (CHFS), for extract new features to select the best features due to eliminating obscures features, In parallel with Apply a novel hybrid feature extraction of three batch edge detection algorithm and texture from MRI images dataset and optimized with fuzzy 64-bin histogram. In the second stage, we applied a clinical dataset to a stacked hybrid classification(SHC) model to combine Jrip and random forest classifiers with six model evaluations as meta-classifier individually to improve the prediction of clinical diagnosis. At the same stage of improving the classification accuracy of neuroimaging (MRI) dataset images by applying a convolution neural network (CNN) in comparison with traditional classifiers, running on extracted features from images. The authors have collected the clinical dataset of 426 subjects with (1229 potential patient sample) from oasis.org and (MRI) dataset from a benchmark kaggle.com with a total of around ~5000 images each segregated into the severity of Alzheimer's. The datasets evaluated using an explorer set of weka data mining software for the analysis purpose. The experimental show that the proposed model of ‏(CHFS) feature extraction ‏ lead to effectively reduced the false-negative rate with a relatively high overall accuracy with a stack hybrid classification of support vector machine (SVM) as meta-classifier of 96.50% compared to 68.83% of the previous result on a clinical dataset, Besides a compared model of CNN classification on MRI images dataset of 80.21%. The results showed the superiority of our CHFS model in predicting Alzheimer's disease more accurately with the clinical medical dataset in early-stage compared with the neuroimaging (MRI) dataset. The results of the proposed model were able to predict with accurately classify Alzheimer's clinical samples at a low cost in comparison with the MRI-CNN images model at the early stage and get a good indicator for high classification rate for MRI images when applying our proposed model of SHC.

We prove the continuous non-Archimedean (resp. p-adic) Banach space and Hilbert space versions of non-Archimedean (resp. p-adic) Welch bounds proved by M. Krishna. We formulate continuous non-Archimedean and p-adic functional Zauner conjectures.

We prove the non-Archimedean (resp. p-adic) Banach space version of non-Archimedean (resp. p-adic) Welch bounds recently obtained by M. Krishna. More precisely, we prove following results. \begin{enumerate}[\upshape(i)] \item Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying $\left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2$ for all $ \lambda_j \in \mathbb{K}, 1\leq j \leq n$, for all $n \in \mathbb{N}.$ Let $\mathcal{X}$ be a $d$-dimensional non-Archimedean Banach space over $\mathbb{K}$. If $\{\tau_j\}_{j=1}^n$ is any collection in $\mathcal{X}$ and $\{f_j\}_{j=1}^n$ is any collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) satisfying $f_j(\tau_j) =1$ for all $1\leq j \leq n$ and the operator $S_{f, \tau} : \text{Sym}^m(\mathcal{X})\ni x \mapsto \sum_{j=1}^nf_j^{\otimes m}(x)\tau_j^{\otimes m} \in \text{Sym}^m(\mathcal{X})$, is diagonalizable, then \begin{align}\label{NONFUNCTIONALWELCH} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{NONFUNCTIONALWELCH}) as non-Archimedean functional Welch bounds. \item For a prime $p$, let $\mathbb{Q}_p$ be the p-adic number field. Let $\mathcal{X}$ be a $d$-dimensional p-adic Banach space over $\mathbb{Q}_p$. If $\{\tau_j\}_{j=1}^n$ is any collection in $\mathcal{X}$ and $\{f_j\}_{j=1}^n$ is any collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) satisfying $f_j(\tau_j) =1$ for all $1\leq j \leq n$ and there exists $b \in \mathbb{Q}_p$ such that $ \sum_{j=1}^{n}f_j^{\otimes m}(x) \tau_j^{\otimes m} =bx$ for all $ x \in \text{Sym}^m(\mathcal{X}),$ then \begin{align}\label{PADICFUNCTIONALWELCH} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{PADICFUNCTIONALWELCH}) as p-adic functional Welch bounds. \end{enumerate} We formulate non-Archimedean functional and p-adic functional Zauner conjectures.

Human Face and facial parts are the most significant parts as it reveals a person’s true identity. It plays an important role in various biometric applications like crowd analysis, human tracking, photography, cosmetic surgery, etc. There are many techniques are available to detect a facial image. Among them, skin detection is the most popular one. The aim of this paper is to detect first the person's identity from facial image and finally check any spot present the the detected person. The first step is to detect the maximum skin region based on a combination method of RGB and HSV color space model. Next it is to verify the skin areas of human through machine learning approach. The Aggregated Channel Features (ACF) detector is used to identify the different facial parts like eye pairs, nose, and mouth. Bootstrap aggregation decision tree classifier is applied to classify the person’s identity based on Histogram Oriented Gradient (HOG) features value. The experimental results show that the proposed method gives the average 97% accuracy.

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.

Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, we present Spitzer's asymptotic Theorem for each case. We also relate this study to the pricing of Asian options.