Covering Rough Sets in Terms of Topological Bi-Neighbourhoods and Their Applications

Abstract

Neighbourhoods are one of the important topics in topology that relies on two types of neighbours of a point and has many applications in the graph theory and in the sciences and medical sciences. In this work, some types of bi-j-neighbourhoods on generalized bicovering approximation space are introduced. Moreover, some kinds of bicovering rough sets using relations are presented. Some properties of these new types of covering are discussed. Pawlaks’ properties are studied in the case of bicovering approximation space. More properties on different bi-neighbourhoods such as bi-j-neighbourhoods, complementary bi-j-neighbourhoods, and bi-j-adhesions are investigated. A comparison between these new types of $\text{bi}$ -neighbourhoods and $\text{bi}$ -covering is presented with the help of some counterexamples. Finally, we give an application of our results in the rheumatic fever data information by generated topologies.