Reductions of a fuzzy covering decision system

Abstract

This paper discusses the reductions of a fuzzy covering decision system. Firstly, we define a new induced fuzzy covering by a given fuzzy covering and give the algorithm to compute a reduction of the induced fuzzy covering. Then, we discuss the most complete fuzzy description of every element with respect to a fuzzy covering system and the upper and lower approximation defined by it. And then, we introduce information entropy and conditional entropy of the fuzzy covering decision system and define the reduction of fuzzy covering system by means of conditional entropy (special conditional entropy) in consistent (β-consistent and inconsistent) fuzzy covering decision systems. Algorithms are designed to compute the approximate reduction of consistent, β-consistent and inconsistent fuzzy covering decision systems, respectively.