Generalized fuzzy rough sets based on fuzzy coverings

TL;DR

This paper advances fuzzy rough set theory by introducing new approximation operators, concepts for system reduction, and mappings, enabling efficient analysis and simplification of fuzzy covering information systems.

Contribution

It develops a comprehensive theoretical framework for fuzzy covering rough sets, including approximation operators, system mappings, and reduction methods, enhancing computational efficiency.

Findings

New fuzzy covering approximation operators and their properties

Methods for reducing large-scale fuzzy covering systems

Homomorphisms enabling conversion of large to small-scale systems

Abstract

This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation of fuzzy coverings for fuzzy covering rough sets, the concepts of fuzzy subcoverings, the reducible and intersectional elements, the union and intersection operations are provided and their properties are discussed in detail. Afterwards, we introduce the concepts of consistent functions and fuzzy covering mappings and provide a basic theoretical foundation for the communication between fuzzy covering information systems. In addition, the notion of homomorphisms is proposed to reveal the relationship between fuzzy covering information systems. We show how large-scale fuzzy covering information systems and dynamic fuzzy covering information systems can be converted into small-scale ones by means of homomorphisms. Finally, an illustrative example is employed to show that the attribute reduction can be simplified significantly by our proposed approach.