An L-fuzzy rough set model based on L-double fuzzy generalized neighborhood systems

Abstract

Considering L being a commutative quantale, the aim of this paper is to introduce the notion of L-double fuzzy generalized neighborhood systems and then a pair of L-double fuzzy lower and upper approximation operators based on it are defined and discussed. In addition, we discuss and characterize the related L-double rough approximation operators when the L-double fuzzy generalized neighborhood system is serial, reflexive, transitive and unary, respectively. Furthermore, we define and study the double measure of L-double rough approximation that in a certain sense characterizes the quality of the obtained approximation. Finally, we interpreted the operators of double measures of L-double fuzzy lower and upper approximation as an L-double fuzzy topology and an L-double fuzzy co-topology on a set X, respectively.