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Keywords = rough (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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