Rough uniformity of topological rough groups and L-fuzzy approximation groups
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.
Introducing the notion of probabilistic convergence ring, and probabilistic limit ring, our motivations among others are, to focus at two vital issues, such as, (a) to provide characterization…
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…