Rough uniformity of topological rough groups and L-fuzzy approximation groups

Abstract

Starting with an approximation space as the underlying structure, we look at the rough uniformity of a topological rough group. Next, taking L as a complete residuated lattice, we consider L-subgroup and normal L-subgroup of a group to create the L-fuzzy upper rough subgroup, and the L-fuzzy lower rough subgroup within the framework of the L-fuzzy approximation spaces. Here we particularly focus on a category of L-fuzzy upper rough subgroups, and a special kind of category of L-closure groups that arises naturally. We introduce the notion of the L-fuzzy approximation group, and study some of its properties including the usual function space structure for the L-fuzzy approximation spaces. Furthermore, using the notion of an L-fuzzy upper approximation operator, we investigate some categorical connection between the L-fuzzy approximation groups, and the L-closure groups. In a similar fashion, using an L-fuzzy lower approximation operator, we investigate the categorical connection between the L-fuzzy approximation groups, and the L-interior groups.