A Novel Matrix-Based Method for Computing Multigranulation Approximation Operators of Incomplete Data

Abstract

Within multigranulation frameworks, incomplete multigranulation rough sets model (IMGRS) constitutes a theoretically significant generalization that extends the tolerance-based rough set. Three disjoint regions of IMGRS, i.e., positive, boundary and negative regions, provide insight into clustering analysis, rule exaction and attribute reduction. However, it is time-consuming when employing the existing traditional methods to compute approximation operators of IMGRS. To solve this problem, we propose a novel matrix-based method for computing positive, boundary and negative regions of IMGRS. First, we introduce matrices associated with tolerance relations and target concepts, deriving fundamental properties of tolerance relation matrices. Within incomplete multigranulation spaces, we then integrate tolerance relation matrices with characteristic functions to construct two intermediate matrices representing three-way regions within the framework of IMGRS. These intermediate matrices enable the derivation of characteristic functions for three-way regions of IMGRS. Building upon the established matrix operations, we design a novel matrix-based algorithm so as to efficiently compute three-way regions of IMGRS. Finally, we perform extensive experiments comparing our matrix-based method with traditional set-based techniques across increasing size of incomplete data. The experimental results conclusively validate the promising efficiency of our matrix-based approach.