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

Document Type : Research Paper


1 Department of Mathematics, Liaocheng University, Liaocheng, P.R.China

2 School of Computer Science and Technology, Liaocheng University, Liaocheng, P.R.China


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.