Semiring-Valued Fuzzy Sets and F-Transform

Jiří Močkoř
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Jiří Močkoř: Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. Dubna 22, 701 03 Ostrava, Czech Republic

Mathematics, 2021, vol. 9, issue 23, 1-24

Abstract: The notion of a semiring-valued fuzzy set is introduced for special commutative partially pre-ordered semirings, including basic operations with these fuzzy structures. It is showed that many standard M V -algebra-valued fuzzy type structures with standard operations, such as hesitant, intuitionistic, neutrosophic or fuzzy soft sets are, for appropriate semirings, isomorphic to semiring-valued fuzzy sets with operations defined. F-transform and inverse F-transform are introduced for semiring-valued fuzzy sets and properties of these transformations are investigated. Using the transformation of M V -algebra-valued fuzzy type structures to semiring-valued fuzzy sets, the F-transforms for these fuzzy type structures is introduced. The advantage of this procedure is, among other things, that the properties of this F-transform are analogous to the properties of the classical F-transform and because these properties are proven for any semiring-valued fuzzy sets, it is not necessary to prove them for individual fuzzy type structures.

Keywords: partially pre-ordered semiring; semiring-valued fuzzy set; adjoint pair of semirings; F-transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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