Intuitionistic Fuzzy Granular Matrix: Novel Calculation Approaches for Intuitionistic Fuzzy Covering-Based Rough Sets

Abstract

Intuitionistic fuzzy (IF) β-minimal description operators can deal with noise data in the IF covering-based rough set theory. That is to say, they can be used to find data that we need in IF environments. For an IF β-covering approximation space (i.e., an IF environment) with a high cardinality, it would be tedious and complicated to use IF set representations to calculate them. Therefore, it is necessary to find a quick method to obtain them. In this paper, we present the notion of IF β-maximal description based on the definition of IF β-minimal description, along with the concepts of IF granular matrix and IF reduction. Moreover, we propose matrix calculation methods for IF covering-based rough sets, such as IF β-minimal descriptions, IF β-maximal descriptions, and IF reductions. Firstly, the notion of an IF granular matrix is presented, which is used to calculate IF β-minimal description. Secondly, inspired by IF β-minimal description, we give the notion of IF β-maximal description. Furthermore, the matrix representations of IF β-maximal descriptions are presented. Next, two types of reductions for IF β-covering approximation spaces via IF β-minimal and fuzzy β-minimal descriptions are presented, along with their matrix representations. Finally, the new calculation methods are compared with corresponding set representations by carrying out several experiments.