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

In this paper, we consider a commutative quantale L as the truth value table to introduce the notion of L-double fuzzy generalized neighborhood (L-DFGN for short) systems. In addition, we specify and study a pair of L-double rough approximation operators based on L-DFGN systems. Moreover, we study and characterize the related L-double rough approximation (L-DRApprox for short) operators when the L-DFGN system satisfies the conditions of seriality, reflexivity, transitivity, and being unary, respectively. Furthermore, we define and study the measure of L-DRApprox, which characterizes the quality of the obtained approximation. Finally, we interpret 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.