Improved rough approximations based on variable J-containment neighborhoods

Abstract

Classic generalized rough set model in neighborhood systems provides a more general framework for depicting approximations, while it may meet the non-reflexive situations. Some scholars put forward different neighborhoods, such as adhesion neighborhoods (briefly, Pj -neighborhoods), containment neighborhoods (briefly, Cj -neighborhoods), and Ej -neighborhoods. However, not all of them are reflexive. Moreover, the granularity of Pj -neighborhoods and Cj -neighborhoods are too fine, and that of Ej -neighborhoods too coarse. To solve the problem, we aim to design a novel construction approach of neighborhoods, called variable j-containment neighborhoods (briefly, Vβj -neighborhoods), which satisfies the reflexivity and the granularity so flexible that the neighborhood space can adjust the granularity to meet the needs of problems.