scholarly journals On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1485
Author(s):  
Pavel Sevastjanov ◽  
Ludmila Dymova ◽  
Krzysztof Kaczmarek
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Short Paper ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Methodological Problems ◽  
Shafer Theory ◽  
Sets Theory

In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.

scholarly journals Belief and Plausibility Measures on Intuitionistic Fuzzy Sets with Construction of Belief-Plausibility TOPSIS

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Miin-Shen Yang ◽  
Zahid Hussain ◽  
Mehboob Ali
Keyword(s):  
Fuzzy Sets ◽  
Hausdorff Metric ◽  
Similarity Measures ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Imprecise Information ◽  
Shafer Theory ◽  
Better Than

Belief and plausibility measures in Dempster–Shafer theory (DST) and fuzzy sets are known as different approaches for representing partial, uncertainty, and imprecise information. There are several generalizations of DST to fuzzy sets proposed in the literature. But, less generalization of DST to intuitionistic fuzzy sets (IFSs), that can somehow present imprecise information better than fuzzy sets, was proposed. In this paper, we first propose a simple and intuitive way to construct a generalization of DST to IFSs with degrees of belief and plausibility in terms of degrees of membership and nonmembership, respectively. We then give belief and plausibility measures on IFSs and construct belief-plausibility intervals (BPIs) of IFSs. Based on the constructed BPIs, we first use Hausdorff metric to define the distance between two BPIs and then establish similarity measures in the generalized context of DST to IFSs. By employing the techniques of ordered preference similarity to ideal solution (TOPSIS), the proposed belief and plausibility measures on IFSs in the framework of DST enable us to construct a belief-plausibility TOPSIS for solving multicriteria decision-making problems. Some examples are presented to manifest that the proposed method is reasonable, applicable, and well suited in the environment of IFSs in the framework of generalization of DST.

scholarly journals Towards Better Concordance among Contextualized Evaluations in FAST-GDM Problems

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 93
Author(s):  
Marcelo Loor ◽  
Ana Tapia-Rosero ◽  
Guy De Tré
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Heterogeneous Group ◽  
Intuitionistic Fuzzy ◽  
High Level ◽  
Consensus Reaching ◽  
Novel Algorithm

A flexible attribute-set group decision-making (FAST-GDM) problem consists in finding the most suitable option(s) out of the options under consideration, with a general agreement among a heterogeneous group of experts who can focus on different attributes to evaluate those options. An open challenge in FAST-GDM problems is to design consensus reaching processes (CRPs) by which the participants can perform evaluations with a high level of consensus. To address this challenge, a novel algorithm for reaching consensus is proposed in this paper. By means of the algorithm, called FAST-CR-XMIS, a participant can reconsider his/her evaluations after studying the most influential samples that have been shared by others through contextualized evaluations. Since exchanging those samples may make participants’ understandings more like each other, an increase of the level of consensus is expected. A simulation of a CRP where contextualized evaluations of newswire stories are characterized as augmented intuitionistic fuzzy sets (AIFS) shows how FAST-CR-XMIS can increase the level of consensus among the participants during the CRP.

scholarly journals Certain Notions of Neutrosophic Topological K-Algebras

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 234 ◽  
Author(s):  
Muhammad Akram ◽  
Hina Gulzar ◽  
Florentin Smarandache ◽  
Said Broumi
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Point Of View ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Research Article

The concept of neutrosophic set from philosophical point of view was first considered by Smarandache. A single-valued neutrosophic set is a subclass of the neutrosophic set from a scientific and engineering point of view and an extension of intuitionistic fuzzy sets. In this research article, we apply the notion of single-valued neutrosophic sets to K-algebras. We introduce the notion of single-valued neutrosophic topological K-algebras and investigate some of their properties. Further, we study certain properties, including C 5 -connected, super connected, compact and Hausdorff, of single-valued neutrosophic topological K-algebras. We also investigate the image and pre-image of single-valued neutrosophic topological K-algebras under homomorphism.

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