Approximation operators and accuracy measures of rough sets from an infra-topology view.

In this work, our target point is to focus on rough approximation operators generated from infra-topology spaces and examine their features. First, we show how infra-topology spaces are constructed from N j -neighborhood systems under an arbitrary relation. Then, we exploit these infra-topology spaces to form new rough set models and scrutinize their master characterizations. The main advantages of these models are to preserve all properties of Pawlak approximation operators and produce accuracy values higher than those given in several methods published in the literature. One of the unique characterizations of the current approach is that all the approximation operators and accuracy measures produced by the current approach are identical under a symmetric relation. Finally, we present two medical applications of the current methods regarding Dengue fever and COVID-19 pandemic. Some debates regarding the pros and cons of the followed technique are given as well as some upcoming work are proposed.

Knowledge Based on Rough Approximations and Ideals

Topology is a beneficial structure to study the approximation operators in the rough set theory. In this work, we first introduce six new types of neighborhoods with respect to finite binary relations. We study their main properties and show under what conditions they are equivalent. Then we applied these types of neighborhoods to initiate some topological spaces that are utilized to define new types of rough set models. We compare these models and prove that the best accuracy measures are obtained in the cases of i and i. Also, we illustrate that our approaches are better than those defined under one arbitrary relation. To improve rough sets’ accuracy, we define some topological spaces using the idea of ideals. With the help of examples, we demonstrate that our methods are better than some methods studied in some published literature. Finally, we give a real-life application showing the merits of the approaches followed in this manuscript.

Some Topological Approaches for Generalized Rough Sets and Their Decision-Making Applications

The rough set principle was proposed as a methodology to cope with vagueness or uncertainty of data in the information systems. Day by day, this theory has proven its efficiency in handling and modeling many real-life problems. To contribute to this area, we present new topological approaches as a generalization of Pawlak’s theory by using j-adhesion neighborhoods and elucidate the relationship between them and some other types of approximations with the aid of examples. Topologically, we give another generalized rough approximation using near open sets. Also, we generate generalized approximations created from the topological models of j-adhesion approximations. Eventually, we compare the approaches given herein with previous ones to obtain a more affirmative solution for decision-making problems.

Subset neighborhood rough sets

We present a novel kind of neighborhood, named subset neighborhood and denoted as Sρ-neighborhood. It is defined under an arbitrary binary relation using the inclusion relations between Nρ-neighborhoods. We study its relationships with some kinds of neighborhood systems given in the literature. Then, we formulate the concepts of Sρ-lower and Sρ-upper approximations, and Sρ-accuracy and roughness measures based on Sρ-neighborhoods. We show in which cases the Sρ-accuracy measure is the highest among related approximations and investigate under which conditions the Sρ-accuracy and Sρ-roughness measures are monotonic. Moreover, we compare our approach with two existing ones and elucidate the advantages of our technique to obtain accuracy measures under some specific relations. To support the obtained results, we provide two medical examples.

An improvement of rough sets’ accuracy measure using containment neighborhoods with a medical application

The rough set theory is a nonstatistical mathematical approach to address the issues of vagueness and uncertain knowledge. The rationale of this theory relies on associating a subset with two crisp sets called lower and upper approximations which are utilized to determine the boundary region and accuracy measure of that subset. Neighborhoods systems are pivotal technique to reduce the boundary region and improve the accuracy measure. Therefore, we aim through this paper to introduce new types of neighborhoods called containment neighborhoods (briefly, Cj-neighborhoods). They are defined depending on the inclusion relations between j-neighborhoods under arbitrary binary relation. We study their relationships with some previous types of neighborhoods, and determine the conditions under which they are equivalent. Then, we applied Cj-neighborhoods to present the concepts of Cj-lower and Cj-upper approximations and reveal main properties with the help of examples. We also prove that a Cj-accuracy measure is the highest in cases of j=i,〈i〉. Furthermore, we compare our approach with two approaches given in published literatures and show that accuracy measure induced from our technique is the best. Finally, we successfully applied Cj-neighborhoods, Nj-neighborhoods and Ej-neighborhoods in a medical application aiming to classify medical staff in terms of suspected infection with the new corona-virus (COVID-19).