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.

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.

Multi-Target Rough Sets and Their Approximation Computation with Dynamic Target Sets

Multi-label learning has become a hot topic in recent years, attracting scholars’ attention, including applying the rough set model in multi-label learning. Exciting works that apply the rough set model into multi-label learning usually adapt the rough sets model’s purpose for a single decision table to a multi-decision table with a conservative strategy. However, multi-label learning enforces the rough set model which wants to be applied considering multiple target concepts, and there is label correlation among labels naturally. For that proposal, this paper proposes a rough set model that has multiple target concepts and considers the similarity relationships among target concepts to capture label correlation among labels. The properties of the proposed model are also investigated. The rough set model that has multiple target concepts can handle the data set that has multiple decisions, and it has inherent advantages when applied to multi-label learning. Moreover, we consider how to compute the approximations of GMTRSs under a static and dynamic situation when a target concept is added or removed and derive the corresponding algorithms, respectively. The efficiency and validity of the designed algorithms are verified by experiments.

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.

Rough uniformity of topological rough groups and L-fuzzy approximation groups

Starting with an approximation space as the underlying structure, we look at the rough uniformity of a topological rough group. Next, taking L as a complete residuated lattice, we consider L-subgroup and normal L-subgroup of a group to create the L-fuzzy upper rough subgroup, and the L-fuzzy lower rough subgroup within the framework of the L-fuzzy approximation spaces. Here we particularly focus on a category of L-fuzzy upper rough subgroups, and a special kind of category of L-closure groups that arises naturally. We introduce the notion of the L-fuzzy approximation group, and study some of its properties including the usual function space structure for the L-fuzzy approximation spaces. Furthermore, using the notion of an L-fuzzy upper approximation operator, we investigate some categorical connection between the L-fuzzy approximation groups, and the L-closure groups. In a similar fashion, using an L-fuzzy lower approximation operator, we investigate the categorical connection between the L-fuzzy approximation groups, and the L-interior groups.

Maximal rough neighborhoods with a medical application

In this paper, we focus on the main concepts of rough set theory induced from the idea of neighborhoods. First, we put forward new types of maximal neighborhoods (briefly, M σ -neighborhoods) and explore master properties. We also reveal their relationships with foregoing neighborhoods and specify the sufficient conditions to obtain some equivalences. Then, we apply M σ -neighborhoods to define M σ -lower and M σ -upper approximations and elucidate which one of Pawlak's properties are preserved (evaporated) by these approximations. Moreover, we research A M σ -accuracy measures and prove that they keep the monotonic property under any arbitrary relation. We provide some comparisons that illustrate the best approximations and accuracy measures are obtained when σ = ⟨ i ⟩ . To show the importance of M σ -neighborhoods, we present a medical application of them in classifying individuals of a specific facility in terms of their infection with COVID-19. Finally, we scrutinize the strengths and limitations of the followed technique in this manuscript compared with the previous ones.

Topological approach to generate new rough set models

In this paper, we introduce a topological method to produce new rough set models. This method is based on the idea of “somewhat open sets” which is one of the celebrated generalizations of open sets. We first generate some topologies from the different types of $$N_\rho $$ N ρ -neighborhoods. Then, we define new types of rough approximations and accuracy measures with respect to somewhat open and somewhat closed sets. We study their main properties and prove that the accuracy and roughness measures preserve the monotonic property. One of the unique properties of these approximations is the possibility of comparing between them. We also compare our approach with the previous ones, and show that it is more accurate than those induced from open, $$\alpha $$ α -open, and semi-open sets. Moreover, we examine the effectiveness of the followed method in a problem of Dengue fever. Finally, we discuss the strengths and limitations of our approach and propose some future work.

The cost-sensitive approximation of neighborhood rough sets and granular layer selection

Neighborhood rough sets (NRS) are the extended model of the classical rough sets. The NRS describe the target concept by upper and lower neighborhood approximation boundaries. However, the method of approximately describing the uncertain target concept with existed neighborhood information granules is not given. To solve this problem, the cost-sensitive approximation model of the NRS is proposed in this paper, and its related properties are analyzed. To obtain the optimal approximation granular layer, the cost-sensitive progressive mechanism is proposed by considering user requirements. The case study shows that the reasonable granular layer and its approximation can be obtained under certain constraints, which is suitable for cost-sensitive application scenarios. The experimental results show that the advantage of the proposed approximation model, moreover, the decision cost of the NRS approximation model will monotonically decrease with granularity being finer.

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.