Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations

Covering Relations in the Lattice of ^-topologies

A topology ^"i is said to cover another topology T3 if ^Ç^i and no other topology may be included between the two. In this paper, we characterize the relationship between a Tj-topology and its covers. This characterization is used to prove that the lattice of 7\-topologies is both upper and lower semimodular. We also prove that the sublattice generated by the covers of a 7\-topology is isomorph...

Definable Subsets in Covering Approximation Spaces

Covering approximation spaces is a class of important generalization of approximation spaces. For a subset X of a covering approximation space (U, C), is X definable or rough? The answer of this question is uncertain, which depends on covering approximation operators endowed on (U, C). Note that there are many various covering approximation operators, which can be endowed on covering approximat...

Some Separations in Covering Approximation Spaces

Adopting Zakowski’s upper approximation operator C and lower approximation operator C, this paper investigates granularity-wise separations in covering approximation spaces. Some characterizations of granularity-wise separations are obtained by means of Pawlak rough sets and some relations among granularitywise separations are established, which makes it possible to research covering approximat...

Covering Spaces

A multiobjective continuous covering location model

This paper presents a multiobjective continuous covering location problem in fuzzy environment. Because of uncertain covering radius, possibility of covering concept is introduced.Since, the uncertainty may cause risk of uncovering customers; the problemis formulated as a risk management model. The presented model is an extension of the discrete covering location models tocontinuous space. Two ...