Generalized fuzzy rough sets based on fuzzy coverings

摘要

This paper further studies the fuzzy rough sets based on fuzzy coverings. Wefirst present the notions of the lower and upper approximation operators basedon fuzzy coverings and derive their basic properties. To facilitate thecomputation of fuzzy coverings for fuzzy covering rough sets, the concepts offuzzy subcoverings, the reducible and intersectional elements, the union andintersection operations are provided and their properties are discussed indetail. Afterwards, we introduce the concepts of consistent functions and fuzzycovering mappings and provide a basic theoretical foundation for thecommunication between fuzzy covering information systems. In addition, thenotion of homomorphisms is proposed to reveal the relationship between fuzzycovering information systems. We show how large-scale fuzzy coveringinformation systems and dynamic fuzzy covering information systems can beconverted into small-scale ones by means of homomorphisms. Finally, anillustrative example is employed to show that the attribute reduction can besimplified significantly by our proposed approach.