An intuitionistic fuzzy graded covering rough set

Exploring rough sets from the perspective of covering represents a promising direction in rough set theory, where concepts are approximated by substituting of an equivalent relation in classical rough set theory with a covering in covering-based rough set theory. By combining intuitionistic fuzzy (IF) β-neighborhoods induced by an IF β-covering with IF rough sets, this study develops a new rough set model, which is a generalization of the β-neighborhood fuzzy covering rough sets and IF rough sets. First, we present the concepts of IF graded covering and IF graded neighborhood, namely, IF β-covering and IF β-neighborhood, respectively. We propose an IF graded approximation space on the basis of IF graded neighborhood and discuss its uncertainty measures, namely, information entropy and rough entropy. Second, we generalize an IF rough set based on IF relation to one based on the presented IF graded neighborhood and use the distance between two IF sets to characterize the latter. Third, we present the matrix computation method for the upper and lower approximations of the presented IF rough sets based on the IF graded neighborhood. Fourth, from the multi-granulation perspective, we examine the IF graded approximation space, uncertainty measures, IF rough sets, and computation methods for its reducts. Finally, we discuss several generalizations similar to the presented IF covering rough sets.