Hierarchical Structures Based on Fuzzy Similarity Relation

In this paper, on the basis of fuzzy quotient space theory, a theoretical framework of hierarchical structures based on fuzzy similarity relations by fuzzy matrices is proposed. The first, the strictly matrix description is introduced to hierarchical structures by a fuzzy similarity relation induced, and we proved the same hierarchical structures by the fuzzy similarity relation induced in two ways of composition; Secondly, the effective algorithm of getting their hierarchical structures by matrices is proposed, and we get some interesting properties. The algorithm has been validated by an example, and we have an analysis of the computational complexity.