A note on “On generalizing covering approximation space”

A note on modular hyperconvex space

On Covering Approximation Subspaces

Let (U ′; C′) be a subspace of a covering approximation space (U ; C) and X ⊂ U ′. In this paper, we show that C′(X) = C(X)⋂ U ′ and B′(X) ⊂ B(X) ⋂ U ′. Also, C(X) = C′(X)⋂ C(U ′) iff (U ; C) has Property Multiplication. Furthermore, some connections between outer (resp. inner) definable subsets in (U ; C) and outer (resp. inner) definable subsets in (U ′; C′) are established. These results ans...

On Generalizing Pawlak Approximation Operators

This paper reviews and discusses generalizations of Pawlak rough set approximation operators in mathematical systems, such as topological spaces, closure systems, lattices, and posets. The structures of generalized approximation spaces and the properties of approximation operators are analyzed.

A Note on Belief Structures and S-approximation Spaces

We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory...

A Note on Covering by Convex Bodies

A classical theorem of Rogers states that for any convex body K in n-dimensional Euclidean space there exists a covering of the space by translates of K with density not exceeding n log n+n log log n+5n. Rogers’ theorem does not say anything about the structure of such a covering. We show that for sufficiently large values of n the same bound can be attained by a covering which is the union of ...