Rough uniformity of topological rough groups and L-fuzzy approximation groups published in 2022 by T M G Ahsanullah
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.
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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…