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The isomorphic fuzzy relations and fuzzy quotient spaces

This paper discussed the relation between FS and QS by theory of the isomorphism and homomorphism of fuzzy relations, and a main conclusion was reached. First, the following two statements are equivalent: (1) a group of fuzzy equivalence relations which are isomorphic for each other given in universe X; (2) a fuzzy quotient space [X] and a fuzzy quotient structure space ([X],d) given in X. Second, the construction of the fuzzy quotient space is given. The preliminary results have established the connection between fuzzy sets and quotient spaces.