Rough approximation operators based on quantale-valued fuzzy generalized neighborhood systems

Let L be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of L-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system-based approximation operators, L-fuzzyrelation-based approximation operators and L-fuzzycovering-based approximation operators as their specialcircumstances. Therefore, the research on L-fuzzy generalizedneighborhood system-based approximation operators has more generalsignificance. In addition, when the L-fuzzy generalizedneighborhood system is serial, reflexive, unary and transitive,then the corresponding approximation operators are discussed and characterized, respectively.

Keywords:

Fuzzy rough set , fuzzy topology , L-fuzzy generalized neighborhood system , quantale