Hierarchical Structure Analysis of Fuzzy Quotient Space

In this paper,the fuzzy quotient space theory for the cut-relation of fuzzy equivalence relation with any threshold is discussed.A method is proposed for hierarchically constructing normalized isosceles distance function between different quotient spaces.And a hierarchical structure of fuzzy quotient space is constructed.The relation between the operations(intersection and combination)of fuzzy equivalence relation and the synthesis of quotient spaces is discussed.