Fuzzy Mappings and Fuzzy Equivalence Relations

Pyung-Ki Lim, Ga-Hee Choi, Kul Hur
2011 International Journal of Fuzzy Logic and Intelligent Systems  
Equivalence relations and mappings for crisp sets are very well known. This paper attempts an investigation of equivalence relations and mappings for fuzzy sets. We list some concepts and results related to fuzzy relations. We give some examples corresponding to the concept of fuzzy equality and fuzzy mapping introduced by Demirci [1]. In addition, we introduce the notion of preimage and quotient of fuzzy equivalence relations. Finally, we investigate relations between a fuzzy equivalence
more » ... on and a fuzzy mapping. Key Words : fuzzy mapping, fuzzy relation, fuzzy equivalence relation, fuzzy quotient of fuzzy mapping by fuzzy equivalence relation. [8] . Let f : X → Y be an(ordinary) mapping, let A ∈ I X and {A α } α∈Γ ⊂ I X , and let B ∈ I Y and {B α } α∈Γ ⊂ I Y . Then: Result 2.A
doi:10.5391/ijfis.2011.11.3.153 fatcat:4o4h7vjgwfahtoerrqsypn2b5q