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 neighborhood system is introduced and then a pair of lower and upper approximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system-based approximation operators, L-fuzzy relation-based approximation operators and L-fuzzy covering-based approximation operators as their special circumstances. Therefore, the research on L-fuzzy generalized neighborhood system-based approximation operators has more general significance. In addition, when the L-fuzzy generalized neighborhood system is serial, reflexive, unary and transitive, then the corresponding approximation operators are discussed and characterized, respectively.