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.