Rough Semiring-Valued Fuzzy Sets with Application

Jiří Močkoř, Petr Hurtik and David Hýnar
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Jiří Močkoř: Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. Dubna 22, 702 00 Ostrava, Czech Republic
Petr Hurtik: Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. Dubna 22, 702 00 Ostrava, Czech Republic
David Hýnar: Varroc Lighting Systems, Suvorovova 195, 742 42 Šenov u Nového Jičína, Czech Republic

Mathematics, 2022, vol. 10, issue 13, 1-31

Abstract: Many of the new fuzzy structures with complete M V -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 A M V -algebras. The category of complete A M V -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.

Keywords: semiring; AMV -algebra; dual pair of semirings; (?, ? ? )-fuzzy set; (?, ? ? )-fuzzy relation; upper and lower (?, ? ? )-approximation; rough (?, ? ? )-fuzzy set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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