Fuzzy Matrix Computation for Fuzzy Information System to Reduce Attributes

Abstract

Recently, many methods based on fuzzy rough sets are proposed to reduce fuzzy attributes. The common characteristic of these methods is that all of them are based on fuzzy equivalence relation. In other words, the underlying concept of rough sets, indispensability relation, is generalized to fuzzy equivalence relation. Here fuzzy equivalence relation is the binary relation, which is reflexive, symmetric and transitive. This paper tries to generalize the fuzzy equivalence relation to fuzzy similarity relation, which is more helpful to keeping the fuzzy information of initial data than fuzzy equivalence relation. Based on the fuzzy similarity relation, fuzzy matrix computation for information system is proposed which can be used to reduce fuzzy attributes. Firstly, fuzzy similarity relation who is isomorphic with the fuzzy similarity matrix is given as fuzzy indispensability relation. Then all the information of initial data, such as the similarity among objects and fuzzy inconsistence degree between two objects, can be represented by fuzzy similarity matrix. Secondly, by considering that the small perturbation of the fuzzy similarity matrix can be ignorable, we propose some basic concepts of knowledge reduction such as fuzzy attributes reduct, core and fuzzy significance of attributes etc in this paper. Thirdly, a heuristic algorithm based on the fuzzy significance of attributes is proposed to find close-to- minimal fuzzy attributes reduct. Finally, experimental comparisons with other methods of attributes reduction are given. The experimental results show that our method is feasible and effective.