An Algebraic Analysis for Binary Intuitionistic L-Fuzzy Relations

Pan, Xiaodong; Xu, Peng

doi:10.1007/978-3-642-37829-4_2

Cited by 2 publications

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“…2 )-fuzzy relations in a set X are isomorphic to L-fuzzy soft relations in a soft space (K, X) defined in [21], and (R 1 , R * 1 )-fuzzy relations are identical to intuitionistic L-fuzzy relations with composition defined in [22,23]. Proposition 3.…”

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confidence: 99%

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Rough Semiring-Valued Fuzzy Sets with Application

Močkoř

Hurtík

Hýnar³

2022

Mathematics

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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.

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confidence: 99%

“…Let (J (X × X), ⊠) be the monoid of all intuitionistic L fuzzy relations in a set X with the composition ⊠ of intuitionistic relations defined in [22], and let (R X×X 1 , ○) be the monoid of all (R 1 , R * 1 )-fuzzy relations in X with the composition ○. Then we have…”

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confidence: 99%