$(O,G)$-granular variable precision fuzzy rough sets based on overlap and grouping functions

TL;DR

This paper introduces a new framework for fuzzy rough sets called $(O,G)$-GVPFRSs, utilizing overlap and grouping functions to improve approximation operators and their representations.

Contribution

The paper develops a novel $(O,G)$-granular variable precision fuzzy rough set model based on overlap and grouping functions, with new approximation expressions and diverse relation representations.

Findings

New $(O,G)$-GVPFRSs framework introduced

Approximation operators expressed via fuzzy implications

Extended conclusions from GVPFRSs to $(O,G)$-GVPFRSs

Abstract

Since Bustince et al. introduced the concepts of overlap and grouping functions, these two types of aggregation functions have attracted a lot of interest in both theory and applications. In this paper, the depiction of $(O,G)$-granular variable precision fuzzy rough sets ($(O,G)$-GVPFRSs for short) is first given based on overlap and grouping functions. Meanwhile, to work out the approximation operators efficiently, we give another expression of upper and lower approximation operators by means of fuzzy implications and co-implications. Furthermore, starting from the perspective of construction methods, $(O,G)$-GVPFRSs are represented under diverse fuzzy relations. Finally, some conclusions on the granular variable precision fuzzy rough sets (GVPFRSs for short) are extended to $(O,G)$-GVPFRSs under some additional conditions.