Theory of Fuzzy Quotient Space (Methods of Fuzzy Granular Computing)
模糊商空间理论(模糊粒度计算方法)

In this paper, the quotient space model is extended to the fuzzy granular world and two main conclusions are given. First, the following four statements are equivalent: (1) a fuzzy equivalence relation given in universe X, (2) a normalized isosceles distance given in quotient space X], (3) a hierarchical structure given in X, (4) a fuzzy knowledge base given in X. Second, the whole world with different fuzzy granularities composes a complete semi-order lattice. The results provide a powerful mathematical model and tool for granule computing.