Fuzzy neighborhood operators and derived fuzzy coverings

Abstract

Fuzzy coverings are natural extensions of the coverings by replacing crisp sets with fuzzy sets. Recently, some fuzzy neighborhood operators based on a fuzzy covering were defined and their properties were investigated by D'eer et al. In this paper, we propose four types of fuzzy neighborhood operators by introducing the notions such as β-neighborhood system, fuzzy β-minimal description and fuzzy β-maximal description. First, we propose these notions and investigate their properties. Then we construct four types of fuzzy neighborhood operators based on the fuzzy β-coverings. Properties and relationship among these four types of fuzzy neighborhood operators are studied. Finally, six types of fuzzy β-coverings were derived by using these four types of fuzzy neighborhood operators and their properties are considered.