Matrix methods for some new covering-based multigranulation fuzzy rough set models under fuzzy complementary β-neighborhoods

Abstract

Fuzzy complementary β-neighborhoods (FCNs) are used to find information relevant to the target in data mining. Based on FCNs, there are six types of covering-based multigranulation fuzzy rough set (CMFRS) models have been constructed, which can be used to deal with the problem of multi-criteria information systems. These CMFRS models are calculated by set representations. However, it is time-consuming and error-prone when set representations are used to compute these CMFRS models in a large multi-criteria information system. Hence, it is important to present a novel method to compute them quickly, which is our motivation for this paper. In this paper, we present the matrix representations of six types of CMFRS models on FCNs. Firstly, some new matrices and matrix operations are given in a multi-criteria information system. Then, matrix representations of three types of optimistic CMFRSs on FCNs are proposed. Moreover, matrix approaches are also used for computing three types of pessimistic CMFRSs on FCNs. Finally, some experiments are presented to show the effectiveness of our approaches.