The Research Of Fuzzy Equivalence Relations In Different Fuzzy Systems

Fuzzy Sets theory is a mathematical approach to deal with fuzzy and uncertaininformation, which was originally proposed by an American Mathematician ProfessorL.A. Zadeh, defining as an extension of Classical Sets theory.Interval-valued fuzzy sets and intuitionistic fuzzy sets are significant extensions ofFuzzy Sets theory by Zadeh. They are more flexible and practical when dealing withthe fuzziness and uncertainty problems, reducing the loss of the fuzzy information.Fuzzy equivalent relation is of great significance in the research of Fuzzy Sets theory.This paper mainly studies the structure of fuzzy equivalence relation in the differentfuzzy relation systems, and thus puts forward the fast algorithm. On the discussion ofdifferent fuzzy relations of reflexivity, symmetry, transitivity, with reference to usingthe relevant properties and calculation methods of all kinds of closures, this paper aimsto construct the fuzzy equivalent relation, and offer the fast algorithm on the basis ofthe instance show that the algorithm can effectively improve the efficiency ofcomputing fuzzy equivalence closure.