Entropy measure for a fuzzy relation and its application in attribute reduction for heterogeneous data

A fuzzy binary relation (for short, fuzzy relation) is a fundamental notion in fuzzy set theory. This paper proposes novel entropy measure for a fuzzy relation and considers its application to attribute reduction for heterogeneous data. We first define a new fuzzy entropy to compute the uncertainty of a fuzzy relation and then put forward the notions of joint information entropy, conditional information entropy and mutual information entropy in an information system with heterogeneous data. The proposed measure can overcome the weakness of the existing measure. Next, we apply the proposed measure to perform attribute reduction in this kind of information systems. Finally, we make experimental analysis to check the feasibility and efficiency of the proposed attribute reduction algorithms. (C) 2022 Elsevier B.V. All rights reserved.