Affiliations: Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia
Correspondence:
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Corresponding author. T. M. G. Ahsanullah, Department of Mathematics, College of Science, King Saud University Riyadh 11451, Saudi Arabia. E-mail: tmga1@ksu.edu.sa.
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.
