Choquet-like Integrals with Multi-Neighborhood Approximation Numbers for Novel Covering Granular Reduction Methods

Abstract

Covering granular reduction is an important issue in multi-covering information systems. The main methods to solve this problem are set operators. How to solve this problem by quantitative analysis is an interesting topic. Furthermore, as a type of nonlinear fuzzy aggregation function (which is a quantitative tool), Choquet-like integrals with fuzzy measures are widely used in many files. However, the corresponding fuzzy measures in Choquet-like integrals are given by man, not by data. In this work, we present two types of multi-neighborhood approximation numbers in multi-covering information systems, which are used to establish Choquet-like integrals. Furthermore, they are applied to deal with the problem of granular reduction in multi-covering information systems. First, the notions of lower and upper multi-neighborhood approximation numbers are presented in a multi-covering information system, as well as their properties. Furthermore, some conditions under which multi-covering information systems induce the same lower and upper multi-neighborhood approximation numbers are presented. Second, two covering granular reduction methods based on multi-neighborhood approximation numbers are presented in multi-covering information systems. Third, multi-neighborhood approximation numbers are used to establish Choquet-like integrals, which are applied in covering granular reduction. Finally, these methods are compared with existing methods through experiments, which are used to demonstrate the effectiveness and benefits of our methods.