On Consistency of Fuzzy Clustering Analysis

This paper presents the concepts of isomorphism and homomorphism of fuzzy sets (fuzzy relation), gives sufficient and necessary conditions of isomorphism and homomorphism of fuzzy sets (fuzzy relation). Fortunately, we point that the essence of fuzzy sets (fuzzy relations) in X ,which give the order relation of elements in X(XtimesX).As long as the corresponding order relations are consistent, conclusions from any fuzzy membership function(fuzzy relation) defined by the order relation are certainly same. We propose the concept of classified isomorphism of the fuzzy relation and prove that if two fuzzy similarity relation are isomorphic, then they must be isomorphic classified by the concept of isomorphic classification of fuzzy relation.