Topological Models of Rough Sets and Decision Making of COVID‐19

Abstract

The basic methodology of rough set theory depends on an equivalence relation induced from the generated partition by the classification of objects. However, the requirements of the equivalence relation restrict the field of applications of this philosophy. To begin, we describe two kinds of closure operators that are based on right and left adhesion neighbourhoods by any binary relation. Furthermore, we illustrate that the suggested techniques are an extension of previous methods that are already available in the literature. As a result of these topological techniques, we propose extended rough sets as an extension of Pawlak’s models. We offer a novel topological strategy for making a topological reduction of an information system for COVID-19 based on these techniques. We provide this medical application to highlight the importance of the offered methodologies in the decision-making process to discover the important component for coronavirus (COVID-19) infection. Furthermore, the findings obtained are congruent with those of the World Health Organization. Finally, we create an algorithm to implement the recommended ways in decision-making.

Topologies on Smashed Twisted Wreath Products of Metagroups

“…Then, it will be interesting to investigate relations of metagroup topologies with topological models of rough sets, because the latter are defined with the help of binary operations, and left and right adhesion sets [38][39][40]. Besides mathematics and computer sciences, they have applications in medicine, economics, etc.…”

Approximations by Ideal Minimal Structure with Chemical Application

“…In the forthcoming, the J MSAS approach will be extended to a variety of other concepts, such as fuzzy sets and soft rough sets. Also, it is planned to benefit from the J MSAS approach to apply them to the problems in [4,8,14,15] to improve their accuracy values.…”

“…Lashin et al [5] used topological notions to study different issues in rough set theory in order to generalize Pawlak's concepts [6] in different applications and integrate the concepts of rough and fuzzy sets. Topological structures were applied in rough sets to improve evolutionary-based feature selection technique using the extension of knowledge [7], decision making of COVID-19 [8,9], and enhanced feature selection based on integration containment neighborhoods rough set approximations and binary honey badger optimization [10]. Several articles [11][12][13][14][15][16][17][18][19] extended the application fields of Pawlak's model.…”

On Fuzzy Point Applications of Fuzzy Topological Spaces

“…Recently, topological structures have been used in many approaches and applications, such as rough sets and their extensions [1][2][3][4][5][6], decision-making problems [7][8][9], medical applications [10][11][12][13][14], topological reduction of attributes for predicting lung cancer and heart failure [15,16], biochemistry [17][18][19][20], fuzzy sets applications [21,22], and bipolar hypersoft classes [23][24][25][26]. Thus, the main goal of this study is to discuss and study some topological structures in fuzzy topological spaces.…”