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In this paper, we present a proposed method for generating a soft rough approximation as a modification and generalization of Zhaowen et al. approach. Comparisons were obtained between our approach and the previous study and also. Eventually, an application on Coronavirus (COVID-19) has been presented, illustrated using our proposed concept, and some influencing results for symptoms of Coronavirus patients have been deduced. Moreover, following these concepts, we construct an algorithm and apply it to a decision-making problem to demonstrate the applicability of our proposed approach. Finally, a proposed approach that competes with others has been obtained, as well as realistic results for patients with Coronavirus. Moreover, we used MATLAB programming to obtain the results;these results are consistent with those of the World Health Organization and an accurate proposal competing with the method of Zhaowen et al. has been studied. Therefore, it is recommended that our proposed concept be used in future decision making. © 2021 Tech Science Press. All rights reserved.

The essential aim of the current work is to enhance the application aspects of Pawlak rough sets. Using the notion of a j-neighborhood space and the related concept of θβ-open sets, different methods for generalizing Pawlak rough sets are proposed and their characteristics will be examined. Moreover, in the context of ideal notion, novel generalizations of Pawlak's models and some of their generalizations are presented. Comparisons between the suggested methods and the previous approximations are calculated. Finally, an application from real-life problems is proposed to explain the importance of our decision-making methods.

The main aims of this paper are to show that some results presented in [1] are erroneous. To this end, we provide some counterexamples to demonstrate our claim, and give the correct form of the incorrect results in [1]. Also, some improvements for the definition of accuracy measure is proposed. Furthermore, we show that the relationships given in the three figures need not be true in general, and determine the conditions under which they are correct. Finally, a medical application in the decision-making of the diagnosis of dengue fever is examined.

The present work proposes new styles of rough sets by using different neighborhoods which are made from a general binary relation. The proposed approximations represent a generalization to Pawlak’s rough sets and some of its generalizations, where the accuracy of these approximations is enhanced significantly. Comparisons are obtained between the methods proposed and the previous ones. Moreover, we extend the notion of “nano-topology”, which have introduced by Thivagar and Richard [49], to any binary relation. Besides, to demonstrate the importance of the suggested approaches for deciding on an effective tool for diagnosing lung cancer diseases, we include a medical application of lung cancer disease to identify the most risk factors for this disease and help the doctor in decision-making. Finally, two algorithms are given for decision-making problems. These algorithms are tested on hypothetical data for comparison with already existing methods.

The core purpose of this paper is to point out some erroneous assertions given in the previous paper ”Idealization ofj-Approximation Spaces”. In fact, we found some shortcomings and errors that need improvement and correction. Firstly, we prove that the relations given in the properties (6) and (7) in Proposition 4.1 are equal, not a subset or superset. Furthermore, we show that items (2), (3), (4), and (6) in Proposition 5.2 are incorrect in general. Additionally, counterexamples are given to confirm our claim. Finally, we illustrate that item (4) in Remarks 5.3 is also incorrect. Moreover, the correct form of the incorrect results in ”Idealization ofj-Approximation Spaces” [22] is presented.&nbsp

Soft rough set theory has been presented as a basic mathematical model for decision-making for many real-life data However, soft rough sets are based on a possible fusion of rough sets and soft sets which were proposed by Feng et al [20] The main contribution of the present article is to introduce a modification and a generalization for Feng's approximations, namely, soft β -rough approximations, and some of their properties will be studied A comparison between the suggested approximations and the previous one [20] will be discussed Some examples are prepared to display the validness of these proposals Finally, we put an actual example of the infections of coronavirus (COVID-19) based on soft β -rough sets This application aims to know the persons most likely to be infected with COVID-19 via soft β -rough approximations and soft β -rough topologies [ABSTRACT FROM AUTHOR] Copyright of Turkish Journal of Mathematics is the property of Scientific and Technical Research Council of Turkey and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use This abstract may be abridged No warranty is given about the accuracy of the copy Users should refer to the original published version of the material for the full abstract (Copyright applies to all Abstracts )

Soft relation is a basic mathematical model that can be related to several real-life data. Throughout many fields, soft relations are used to build soft topological structures. In addition, soft topological constructs are generalized methods to calculate similarity and dissimilarity of objects. Within this article, we present a new approach for directly producing a soft topology by soft relation without using base or subbase. This process is important technique for applications of soft topology. There is investigations into the relationship between soft set topologies and different relations and some of their properties are obtained.

A human heart is represented by graph theory and has many topological formulations. The main purpose of the article is to introduce a special class of neighborhood systems, called $1$-neighborhood systems ($\NS$s for short), as tools to generalize rough set theory and give the human heart new modeling by using topological structures. Some new types of minimal neighborhoods and core minimal are introduced. A comparison between these new types of neighborhoods are discussed. In addition, new forms of topological spaces through a $1$-$\NS$ of vertices for a graph of the human heart are presented and studied as a practical example in real-life problems. A best model of the topological structure which may be used for diagnosis is suggested.

The main goal of this paper is to integrate the relationships among rough set theory and topology. We introduce different closure operators by using binary relations. Using these operators, we construct generalized approximation operators in the theory of rough sets. In addition, new methods for generating different topologies from any binary relation (without using base or subbase) are provided. The main properties of suggested structures are investigated. Comparisons among the suggested operations and the previous works are constructed. The suggested methods depend, basically, on the “j-neighborhood space” that given by (Abd El-Monsef et al., Int J Granul Comput Rough Sets Intell Syst 3:292–305, 2014). These methods generate new granulation for rough sets. Finally, a practical example is introduced as a simple application for the suggested structures. We think that at the level of theoretical foundations and real-life implementations, the proposed approaches place emphasis on ties between rough sets, granular computing, and information discovery and data mining.

Covering-based rough sets are important generalizations of the classical rough sets of Pawlak. In this paper, by means of j-neighborhoods, complementary j-neighborhoods and j-adhesions, we build some new different types of j-covering approximations based rough sets and study related properties. Also, we explore the relationships between the considered j-covering approximations and investigate the properties of them. Using different neighborhoods, some different general topologies are generated as topologies induced from a binary relation. Finally, an interesting application of the new types of covering-based rough sets to the rheumatic fever is given.

Soft rough set model represents a different mathematical model to which many real-life data can be connected. In fact, this theory represents a link between soft set and rough set theories. The main goal of the present paper is to introduce a new approach to modify and generalize soft rough sets. We are discussing and exploring the basic properties for these approaches. In addition, we use the suggested approaches as a mathematical modeling for an uncertain data and deal with the ambiguity. Comparisons among the proposed methods and the previous one are obtained. Finally, a medical application of the suggested approximations in decision making of diagnosis of COVID-19 is illustrated. Moreover, we develop an algorithm following these concepts and apply it to a decision making problem to demonstrate the applicability of the proposed methods.

Approximation space can be said to play a critical role in the accuracy of the set’s approximations. The idea of “approximation space” was introduced by Pawlak in 1982 as a core to describe information or knowledge induced from the relationships between objects of the universe. The main objective of this paper is to create new types of rough set models through the use of different neighborhoods generated by a binary relation. New approximations are proposed representing an extension of Pawlak’s rough sets and some of their generalizations, where the precision of these approximations is substantially improved. To elucidate the effectiveness of our approaches, we provide some comparisons between the proposed methods and the previous ones. Finally, we give a medical application of lung cancer disease as well as provide an algorithm which is tested on the basis of hypothetical data in order to compare it with current methods.

In this paper, we shall integrate some ideas in terms of concepts in topology. First, we introduce some new concepts of rough membership relations and functions in the generalized covering approximation space. Second, we introduce some topological applications namely “near concepts” in the generalized covering approximation space. Accordingly, several types of fuzzy sets are constructed. The basic notions of near approximations are introduced and sufficiently illustrated. Near concepts are provided to be easy tools to classify the sets and to help for measuring exactness and roughness of sets. Many proved results, examples and counter examples are provided. Finally, we give two practical examples to illustrate our approaches.

In this paper, we present the covering rough sets based on neighborhoods by approximation operations as a new type of extended covering rough set models. In fact, we have introduced generalizations to W. Zhu approaches (Zhu, 2007). Based on the notion of neighborhood induced from any binary relation, four different pairs of dual approximation operators are defined with their properties being discussed. The relationships among these operators are investigated. Finally, an interesting theorem to generate different topologies is provided. Comparisons between these topologies are discussed. In addition, several examples and counter examples to indicate counter connections are investigated.

The present paper is devoted to discussion of extended covering rough sets from the relations point of view. In fact, we give new definitions to the lower and the upper approximations using a binary general relation. Moreover, our approach represent new generalizations of Pawlak approaches. New closure operators derived from relation are investigated too. AMS Subject Classification: 54A05, 54B05, 54C05

In this paper, for the first time, we introduce and study the new concepts near closure operators induced from binary relation. These operators represent a generalization to closure operators that are induced from binary relations. The suggested techniques will narrow the gap between topologists and those who are interested in applications with topology in their field. The fundamental properties of the suggested structures are obtained. Finally, we introduce some applications of the suggested structures in rough set theory. Moreover, we give a simple practical example to illustrate the importance of near concepts in rough set theory and we introduce comparisons between our approaches and other approaches.

Considering the generalised approximation space, this paper aims to introduce and study eight approaches for approximating rough sets. The approximations are based on different topologies. Comparisons between the accuracy of these types of approximations are superimposed. Some fundamental properties of the suggested approximation operators are obtained.