Hierarchical structures based on intuitionistic fuzzy tolerance relations

In this paper, on the basis of fuzzy quotient space theory, a theoretical framework of hierarchical structures based on intuitionistic fuzzy tolerance relations by intuitionistic fuzzy tolerance matrices is proposed. The first, the strictly matrix which is induced by an intuitionistic fuzzy tolerance relation describes hierarchical structures, we prove the same hierarchical structure induced in two ways of composition by the intuitionistic fuzzy tolerance relations, and we get some interesting properties; secondly, the effective algorithm of getting their hierarchical structures by matrices is proposed. The algorithm has been validated by an example.