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Keywords = (ℛ, ℛ∗)-fuzzy set

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31 pages, 1528 KiB  
Article
Rough Semiring-Valued Fuzzy Sets with Application
by Jiří Močkoř, Petr Hurtik and David Hýnar
Mathematics 2022, 10(13), 2274; https://doi.org/10.3390/math10132274 - 29 Jun 2022
Cited by 6 | Viewed by 1906
Abstract
Many of the new fuzzy structures with complete MV-algebras as value sets, such as hesitant, intuitionistic, neutrosophic, or fuzzy soft sets, can be transformed into one type of fuzzy set with values in special complete algebras, called AMV-algebras. [...] Read more.
Many of the new fuzzy structures with complete MV-algebras as value sets, such as hesitant, intuitionistic, neutrosophic, or fuzzy soft sets, can be transformed into one type of fuzzy set with values in special complete algebras, called AMV-algebras. The category of complete AMV-algebras is isomorphic to the category of special pairs (R,R) of complete commutative semirings and the corresponding fuzzy sets are called (R,R)-fuzzy sets. We use this theory to define (R,R)-fuzzy relations, lower and upper approximations of (R,R)-fuzzy sets by (R,R)-relations, and rough (R,R)-fuzzy sets, and we show that these notions can be universally applied to any fuzzy type structure that is transformable to (R,R)-fuzzy sets. As an example, we also show how this general theory can be used to determine the upper and lower approximations of a color segment corresponding to a particular color. Full article
(This article belongs to the Special Issue FSTA: Fuzzy Set Theory and Applications)
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6 pages, 246 KiB  
Proceeding Paper
Fuzzy Inference Full Implication Method Based on Single Valued Neutrosophic t-Representable t-Norm
by Minxia Luo, Donghui Xu and Lixian Wu
Proceedings 2022, 81(1), 24; https://doi.org/10.3390/proceedings2022081024 - 11 Mar 2022
Viewed by 1969
Abstract
As a generalization of intuitionistic fuzzy sets, single-valued neutrosophic sets have certain advantages for solving indeterminate and inconsistent information. In this paper, we study the fuzzy inference full implication method based on a single-valued neutrosophic t-representable t-norm. Firstly, single-valued neutrosophic fuzzy inference triple [...] Read more.
As a generalization of intuitionistic fuzzy sets, single-valued neutrosophic sets have certain advantages for solving indeterminate and inconsistent information. In this paper, we study the fuzzy inference full implication method based on a single-valued neutrosophic t-representable t-norm. Firstly, single-valued neutrosophic fuzzy inference triple I principles for fuzzy modus ponens and fuzzy modus tollens are shown. Then, single-valued neutrosophic -type triple I solutions for fuzzy modus ponens and fuzzy modus tollens are given. Finally, the robustness of the full implication of the triple I method based on a left-continuous single-valued neutrosophic t-representable t-norm is investigated. As a special case in the main results, the sensitivities of full implication triple I solutions, based on three special single-valued neutrosophic t-representable t-norms, are given. Full article
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