Fuzzy Equivalent Matrices in Fuzzy Clustering
模糊聚类中的模糊等价矩阵

The following problems have been discussed. First, based on the theory of distribution structure of fuzzy similar matrix equation X 2=X , the existence theorem and local uniqueness theorem of the optimal fuzzy equivalent matrix have been proved by using the method of abstract analysis. Second, the relation between local optimal fuzzy equivalent matrix and the given fuzzy similar matrix has been pointed out. Third, the relation between transitive closure and optimal fuzzy equivalent matrix has been discussed. At last, the concept of transitive kernel is proposed.