Reduction approaches for fuzzy covering systems

Abstract

A β-covering is an extension of many types of coverings, such as partitions, coverings, and fuzzy coverings. It provides effective approaches to deal with uncertain and fuzzy information. In this paper, we investigate the reduction problem for fuzzy β covering systems and fuzzy β covering decision systems. We propose a reduction algorithm for a fuzzy β covering system such that existing reduction algorithms for a covering system represent a special case. In the existing definition of fuzzy β covering decision systems, the decision attribute must be an equivalence relation; this requirement remains a restriction for applications. To address the issue, we further generalize the definition so that the decision attribute no longer needs to be an equivalence relation. For such fuzzy β covering decision systems, we propose a new discernibility matrix and provide a unified attribute reduction algorithm to identify all reducts. Our work extends the scope of application of attribute reduction. Finally, we use 21 public datasets to verify the effectiveness and feasibility of the proposed algorithms.