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

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...

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Autores principales:	Pavel Sevastjanov, Ludmila Dymova, Krzysztof Kaczmarek
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	novel fuzzy sets theories intuitionistic fuzzy sets Dempster–Shafer theory Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/0ece269ea6314a5b8f49045cf041503d
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id	oai:doaj.org-article:0ece269ea6314a5b8f49045cf041503d
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spelling	oai:doaj.org-article:0ece269ea6314a5b8f49045cf041503d2021-11-25T17:30:02ZOn the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss10.3390/e231114851099-4300https://doaj.org/article/0ece269ea6314a5b8f49045cf041503d2021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1485https://doaj.org/toc/1099-4300In 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.Pavel SevastjanovLudmila DymovaKrzysztof KaczmarekMDPI AGarticlenovel fuzzy sets theoriesintuitionistic fuzzy setsDempster–Shafer theoryScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1485, p 1485 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	novel fuzzy sets theories intuitionistic fuzzy sets Dempster–Shafer theory Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	novel fuzzy sets theories intuitionistic fuzzy sets Dempster–Shafer theory Science Q Astrophysics QB460-466 Physics QC1-999 Pavel Sevastjanov Ludmila Dymova Krzysztof Kaczmarek On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss
description	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.
format	article
author	Pavel Sevastjanov Ludmila Dymova Krzysztof Kaczmarek
author_facet	Pavel Sevastjanov Ludmila Dymova Krzysztof Kaczmarek
author_sort	Pavel Sevastjanov
title	On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss
title_short	On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss
title_full	On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss
title_fullStr	On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss
title_full_unstemmed	On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss
title_sort	on the neutrosophic, pythagorean and some other novel fuzzy sets theories used in decision making: invitation to discuss
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/0ece269ea6314a5b8f49045cf041503d
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On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

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