Theory of Fuzzy Quotient Space (Methods of Fuzzy Granular Computing)
Ling Zhang, Bo Zhang · 2003
Received 2002-07-29; Accepted 2002-09-30 Zhang L, Zhang B. Theory of fuzzy quotient space (methods of fuzzy granular computing). Journal of Software, 2003,14(4):770~776. Abstract: 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. Key words: granule computing; quotient space theory of problem solving; rough set theory; fuzzy set theory; quotient