Comparison of six types of rough approximations based on j-neighborhood space and j-adhesion neighborhood space

The accurate diagnosis for COVID-19 variants using nearly initial-rough sets

The rapid evolution of rough-set theory has prompted the need for enhanced methodologies in medical diagnostics, particularly regarding COVID-19 variant detection. This study introduces refined mathematical techniques based on topological structures (called nearly initial-rough sets) derived directly from initial-rough sets. Four categories of rough-set methodologies are presented, demonstrating heightened accuracy through comprehensive comparisons against existing methods. By leveraging these techniques, a rule-based classification system for COVID-19 variants is established, achieving 100 % accuracy measures through rigorous testing against real-world and computer-generated data. The implications of these advancements in medical diagnosis hold promise for future research, offering accessible and precise tools for variant identification and prediction. Using a medical application as a case study, we demonstrate superiority through comparative analyses, aligning mathematical results with medical data and showcasing the potential for broader applications beyond experts in topology. Furthermore, the study outlines an algorithm simplifying implementation, particularly in MATLAB, and suggests future explorations in medical, economic, and diverse theoretical frameworks to enhance applicability.

Improved rough approximations based on variable J-containment neighborhoods

Classic generalized rough set model in neighborhood systems provides a more general framework for depicting approximations, while it may meet the non-reflexive situations. Some scholars put forward different neighborhoods, such as adhesion neighborhoods (briefly, P j -neighborhoods), containment neighborhoods (briefly, C j -neighborhoods), and E j -neighborhoods. However, not all of them are reflexive. Moreover, the granularity of P j -neighborhoods and C j -neighborhoods are too fine, and that of E j -neighborhoods too coarse. To solve the problem, we aim to design a novel construction approach of neighborhoods, called variable j-containment neighborhoods (briefly, V j β -neighborhoods), which satisfies the reflexivity and the granularity so flexible that the neighborhood space can adjust the granularity to meet the needs of problems. We generalize three kinds of rough approximations in V j β -neighborhood spaces and discuss their properties. What's more, we analyze the topology structures relying on V j β -neighborhood spaces and compare our proposed approach with the existing approaches. By selecting the appropriate parameter β , our neighborhood system is more flexible in adjusting the granularity to fit problem requirements. And illustrative examples demonstrate the advantages of the proposed rough set model to attribute reduction in incomplete information systems.

A further study on generalized neighborhood systems-based pessimistic rough sets

The generalized neighborhood system-based rough set is an important extension of Pawlak’s rough set. The rough sets based on generalized neighborhood systems include two basic models: optimistic and pessimistic rough sets. In this paper, we give a further study on pessimistic rough sets. At first, to regain some properties of Pawlak’s rough sets that are lost in pessimistic rough sets, we introduce the mediate, transitive, positive (negative) alliance conditions for generalized neighborhood systems. At second, some approximation operators generated by special generalized neighborhood systems are characterized, which include serial, reflexive, symmetric, mediate, transitive, and negative alliance generalized neighborhood systems and their combinations (e.g. reflexive and transitive). At third, we discuss the topologies generated by the upper and lower approximation operators of the pessimistic rough sets. Finally, combining practical examples, we apply pessimistic rough sets to rule extraction of incomplete information systems. Particularly, we prove that different decision rules can be obtained when different neighborhood systems are chosen. This enables decision makers to choose decisions based on personal preferences.

Covering soft rough sets and its topological properties with application

In this article, we introduce the notion of the complementary soft neighborhood and present three kinds of covering soft rough set ($$\mathcal {CSR}$$ CSR ) models. The basic properties of these models are investigated. The relationships among these models are also discussed. Moreover, we establish the topological approach to $$\mathcal {CSR}$$ CSR say, $$\varDelta $$ Δ -topological spaces (i.e., $$\varDelta $$ Δ -TS). Hence, the topological properties for $$\varDelta $$ Δ -TS models such as $$\varDelta $$ Δ -open sets, $$\varDelta $$ Δ -closed sets, $$\varDelta $$ Δ -interior, $$\varDelta $$ Δ -closure, $$\varDelta $$ Δ -boundary, $$\varDelta $$ Δ -neighborhood and $$\varDelta $$ Δ -limit point are studied and the relationships between them are given. Finally, we make use of an algorithm for these proposed models to deal with uncertainties for solving the MGDM problems using the constructed topologies.

Uncertainty measure for Z-soft covering based rough graphs with application

Soft graphs are an interesting way to represent specific information. In this paper, a new form of graphs called Z-soft covering based rough graphs using soft adhesion is defined. Some important properties are explored for the newly constructed graphs. The aim of this study is to investigate the uncertainty in Z-soft covering based rough graphs. Uncertainty measures such as information entropy, rough entropy and granularity measures related to Z-soft covering-based rough graphs are discussed. In addition, we develop a novel Multiple Attribute Group Decision-Making (MAGDM) model using Z-soft covering based rough graphs in medical diagnosis to identify the patients at high risk of chronic kidney disease using the collected data from the UCI Machine Learning Repository.

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

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.

Cq-ROFRS: covering q-rung orthopair fuzzy rough sets and its application to multi-attribute decision-making process

Pythagorean fuzzy sets (briefly, PFSs) were created as an upgrade to intuitionistic fuzzy sets (briefly, IFSs) which helped to address some problems that IFSs couldn’t solve. The definition of q-rung orthopair fuzzy sets (briefly, q-ROFS) is then declared to generalize and solve PFS and IFS failures. Using the concept of PF $$\beta $$ β -neighborhood, Zhan et al. defined the description of the covering through the Pythagorean fuzzy rough set (briefly, CPFRS). Hussain et al. also developed the concept of q-ROF $$\beta $$ β -neighborhood to build the concept of covering through q-rung orthopair fuzzy rough sets (Cq-ROFRS). To enhance the results in Zhan et al.’s and Hussain et al.’s method and in a related context, the concept of PF complementary $$\beta $$ β -neighborhood is constructed. Hence, using PF $$\beta $$ β -neighborhood and PF complementary $$\beta $$ β -neighborhood, three novel kinds of CPFRS are investigated and the related characteristics are analyzed. The interrelationships between Zhan et al.’s approach and our approaches are also discussed. Besides, the concept of q-ROF complementary $$\beta $$ β -neighborhood is examined. Three new Cq-ROFRS models are differentiated using the principles of q-ROF $$\beta $$ β -neighborhood and q-ROF complementary $$\beta $$ β -neighborhood. As a result, the related properties and relationships between these various models and Hussain et al.’s model are established. Because of these correlations, we may consider our approach to be a generalization of Zhan et al.’s and Hussain et al’s approaches. Finally, we developed applications to solve MADM problems using CPFRS and Cq-ROFRS, as well as variances of the two methods using numerical examples are presented.

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.

Corrigendum to “Comparison of six types of rough approximations based on j-neighborhood space and j-adhesion neighborhood space"

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.

A topological reduction for predicting of a lung cancer disease based on generalized rough sets

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.

Graded rough sets based on neighborhood operator over two different universes and their applications in decision-making problems

In this paper, we will propose the novel notion of neighborhood rough sets on a universe set and study some of their basic properties. Then, the relationships between the neighborhood rough sets and covering rough sets are established. Further, the several related notions of probabilistic neighborhood rough sets are investigated and their basic theoretical are discussed. In addition, the notion of neighborhood rough sets over two different universes is defined, and interesting in their properties are explained. Depend on the neighborhood rough sets over two different universes, two algorithms are designed to solve the rough decision-making problems and clarify their applicability by two illustrative examples, respectively. Finally, a comparison between Liu et al.’s approach and our approach is given.

A comparison of two types of rough approximations based on Nj-neighborhoods

In 1982, Pawlak proposed the concept of rough sets as a novel mathematical tool to address the issues of vagueness and uncertain knowledge. Topological concepts and results are close to the concepts and results in rough set theory; therefore, some researchers have investigated topological aspects and their applications in rough set theory. In this discussion, we study further properties of Nj-neighborhoods; especially, those are related to a topological space. Then, we define new kinds of approximation spaces and establish main properties. Finally, we make some comparisons of the approximations and accuracy measures introduced herein and their counterparts induced from interior and closure topological operators and E-neighborhoods.

Certain types of fuzzy soft β-covering based fuzzy rough sets with application to decision-making

The aim of this paper is to introduce and study different kinds of fuzzy soft β-neighborhoods called fuzzy soft β-adhesion neighborhoods and to analyze some of their properties. Further, the concepts of soft β-adhesion neighborhoods are investigated and the related properties are studied. Then, we present new kinds of lower and upper approximations by means of different fuzzy soft β-neighborhoods. The relationships among our models (i.e., Definitions 3.9, 3.12, 3.15 and 3.18) and Zhang models [48] are also discussed. Finally, we construct an algorithm based on Definition 3.12, when k = 1 to solve the decision-making problems and illustrate its applicability through a numerical example.