On the Granular Representation of Fuzzy Quantifier-Based Fuzzy Rough Sets

TL;DR

This paper investigates the granular representation of fuzzy rough sets based on fuzzy quantifiers, showing that certain models like Sugeno-based FRS can always be granularly represented, aiding in handling data inconsistencies.

Contribution

It extends the understanding of granular representations in fuzzy rough sets, especially for models based on Choquet and Sugeno fuzzy quantifiers, under various conditions.

Findings

Choquet-based fuzzy rough sets can be granularly represented under specific conditions.

Sugeno-based fuzzy rough sets always admit granular representation.

Granular representations help in resolving data inconsistencies and managing noise.

Abstract

Rough set theory is a well-known mathematical framework that can deal with inconsistent data by providing lower and upper approximations of concepts. A prominent property of these approximations is their granular representation: that is, they can be written as unions of simple sets, called granules. The latter can be identified with "if. . . , then. . . " rules, which form the backbone of rough set rule induction. It has been shown previously that this property can be maintained for various fuzzy rough set models, including those based on ordered weighted average (OWA) operators. In this paper, we will focus on some instances of the general class of fuzzy quantifier-based fuzzy rough sets (FQFRS). In these models, the lower and upper approximations are evaluated using binary and unary fuzzy quantifiers, respectively. One of the main targets of this study is to examine the granular representation of different models of FQFRS. The main findings reveal that Choquet-based fuzzy rough sets can be represented granularly under the same conditions as OWA-based fuzzy rough sets, whereas Sugeno-based FRS can always be represented granularly. This observation highlights the potential of these models for resolving data inconsistencies and managing noise.