ARTICLE | doi:10.20944/preprints201706.0061.v1
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: generalized triangular intuitionistic fuzzy geometric aggregation operator; triangular intuitionistic fuzzy number; intuitionistic fuzzy set; multi-criteria decision-making; attitudinal character; flexibility
Online: 14 June 2017 (05:55:52 CEST)
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.
ARTICLE | doi:10.20944/preprints201811.0226.v1
Subject: Mathematics & Computer Science, Logic Keywords: intuitionistic logic; quantum computing; Kripke-style semantics
Online: 9 November 2018 (03:03:59 CET)
We know that quantum logics are the most prominent logical systems associated to the lattices of closed Hilbert subspaces. But what does it happen if, following a quantum computing perspective, we want to associate a logic to the process of quantum registers measurements? This paper gives an answer to this question, and, quite surprising, shows that such a logic is nothing else that the standard propositional intuitionistic logic.
ARTICLE | doi:10.20944/preprints202001.0102.v2
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: non-standard analysis; topos theory; artificial intelligence; brain studies; intuitionistic logic
Online: 3 August 2020 (08:24:27 CEST)
This work promotes new methods in Mathematical Modeling, consisting in the use of the methods of Non-standard Analysis in Topoi, having as its main purpose, the mathematical definitions of the pseudoparticles from the title, with arguments from Biology/Physiology (Mathematical Neuroscience), Physics (String Theory and Emergent Quantum Mechanics), and Cybernetics (Global Brain, including Natural and Artificial Intelligence). The connections between brain and mind will be scketched via the genetic/epigenetic interplay. The topoi model the intuitionistic logic (multi-valued) and have been used in Quantum Physics while Non-Standard Analysis in SET (= the Category of sets) has been applied in Mathematical Economics; topics from Theory of Categories were also used in the study of Consciousness; however, the combination topoi - non-standard analysis was never used until now in Applied Mathematics. Another important objective is to produce progress in this aria of Pure Mathematics also - the build of non-standard analysis in classes of topoi, already used in Physics. We propose the logic of non-standard extensions in topoi as a model of the human thinking (based on infons/receptons), these theories representing new top and very difficult results in Abstract Mathematics either.
ARTICLE | doi:10.20944/preprints201810.0443.v1
Subject: Mathematics & Computer Science, Other Keywords: group decision makers; multicriteria analysis; performance evaluation; internet of things; intuitionistic environment
Online: 19 October 2018 (08:08:19 CEST)
The performance evaluation of the Internet of Things (IoT) based supply chain is challenging due to the involvement of multiple decision makers, the multi-dimensional nature of the evaluation process, and the existence of uncertainty and imprecision in the decision making process. To ensure effective decisions are made, this paper presents a fuzzy multicriteria analysis model for evaluating the performance of IoT based supply chain. The inherent uncertainty and imprecision of the performance evaluation process is adequately handled by using intuitionistic fuzzy numbers. A new algorithm is developed for determining the overall performance index for each alternative across all criteria. The development of the fuzzy multicriteria group decision making model provides organizations with the ability to effectively evaluate the performance of their IoT based supply chains for improving their competitiveness. An example is presented for demonstrating the applicability of the model for dealing with real world IoT-based performance evaluation problems.
ARTICLE | doi:10.20944/preprints201805.0296.v1
Subject: Mathematics & Computer Science, Other Keywords: normal intuitionistic fuzzy numbers; Heronian mean; Hamacher t-conorm; Hamacher t-norm
Online: 22 May 2018 (10:15:21 CEST)
Hamacher operation which is generalization of the Algebraic and Einstein operation, can widely provide a large number of arithmetical operation with respect to uncertainty information, and Heronian mean can deal with correlations of the input arguments or different criteria and don’t make calculation redundancy, meanwhile, the normal intuitionistic fuzzy numbers (NIFNs) can depict distinctively normal distribution information in practical decision making. In this paper, a multi-criteria group decision-making (MCGDM) problem is researched under the NIFNs environment, and a new MCGDM approach is introduced on the basis of the Hamacher operation. Firstly, according to Hamacher t-conorm and t-norm, some operational laws of NIFNs are presented. Secondly, it is noticed that Heronian mean can’t only once take into account mutual relation between attribute values once, but also consider the correlation between input argument and itself. Therefore, we develop some operators and study their properties in order to aggregate normal intuitionistic fuzzy numbers information, these operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM) and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we apply the proposed operators to the MCGDM problem and present a new method. The main characteristics of this new method involve that: (1) it is suitable to make decision under the normal intuitionistic fuzzy numbers environment and more reliable and reasonable to aggregate the normal distribution information. (2) it utilizes Hamacher operation which can provide more reliable and flexible decision-making results and offer an effective and powerful mathematic tool for the MAGDM under uncertainty. (3) it uses the Heronian mean operator which can considers relationships between the input arguments or the attributes and don’t brings subsequently about redundancy. Lastly, an application is given for showing the feasibility and effectiveness of the presented method in this paper.
ARTICLE | doi:10.20944/preprints201807.0405.v1
Subject: Mathematics & Computer Science, Numerical Analysis & Optimization Keywords: interval-valued intuitionistic fuzzy set; aggregation operator; Heronian mean; geometric Heronian mean; multi-attribute decision making
Online: 23 July 2018 (05:29:46 CEST)
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.
ARTICLE | doi:10.20944/preprints202108.0129.v1
Subject: Physical Sciences, Mathematical Physics Keywords: Region based theory of space; RBTS; Contact algebra; Dyadic and Triadic relations; sequent algebra; boundaries; triple junctions; mereotopology; 4D mereotopology; mereophysics; Region Connect Calculus RCC; invariant spacetime interval; Falaco solitons; phase-field method; intuitionistic logic
Online: 5 August 2021 (08:39:00 CEST)
Mereotopology is a concept rooted in analytical philosophy. The phase-field concept is based on mathematical physics and finds applications in materials engineering. The two concepts seem to be disjoint at a first glance. While mereotopology qualitatively describes static relations between things like x isConnected y (topology) or x isPartOf y (mereology) by first order logic and Boolean algebra, the phase-field concept describes the geometric shape of things and its dynamic evolution by drawing on a scalar field. The geometric shape of any thing is defined by its boundaries to one or more neighboring things. The notion and description of boundaries thus provides a bridge between mereotopology and the phase-field concept. The present article aims to relate phase-field expressions describing boundaries and especially triple junctions to their Boolean counterparts in mereotopology and contact algebra. An introductory overview on mereotopology is followed by an introduction to the phase-field concept already indicating first relations to mereo- topology. Mereotopological axioms and definitions are then discussed in detail from a phase-field perspective. A dedicated section introduces and discusses further notions of the isConnected relation emerging from the phase-field perspective like isSpatiallyConnected, isTemporallyConnected, isPhysicallyConnected, isPathConnected and wasConnected. Such relations introduce dynamics and thus physics into mereotopology as transitions from isDisconnected to isPartOf can be described.