Soft Rough Sets Research Articles

Covering rough set models, fuzzy rough set models and soft rough set models induced by covering similarity

In order to study the rule of quantity characteristics of rough set theory, a novel notion of covering similarity in a covering approximation space is introduced. Based on this new notion, novel covering rough set models, novel fuzzy rough set models and novel soft rough set models are defined. Further, the concept of similarity matrix is presented, and then the matrix calculation formulas of all the new concepts and new models are deduced. Moreover, aim to better solve the practical problems by comparing the similarity, a concept of similarity interval is introduced, then the covering classification is carried out and a partial order of all the classes is derived. Finally, a few practical examples are given to illustrate the simple applications of all the new concepts and models in this paper.

Autism Detection Using Fuzzy β-Neighborhood Based Soft Rough Sets

Autism Spectrum Disorder refers to a variety of conditions represented by complications in social skills, limited interests and communication that’s majoritarily non-verbal. The early signs and symptoms of the disorder were found to be noticeable at a young age. However, the clinical tests take longer to diagnose and come at a higher cost. As a result, in recent years, several studies have been made to enable autism detection through early intervention. Rough Set theory is one such efficient mathematical tool for this application. This paper introduces the concept of fuzzy-neighborhood based soft rough sets The major advantage of introducing this concept lies in the construction of fuzzy -neighborhood of each object obtained through its -reduct. This neighborhood captures those objects having similar characteristics with respect to the significant attributes. The application of this model is highlighted through autism detection by obtaining the neighborhood of the given image. The proposed model also efficiently captures the various levels of autism with great accuracy. The validation is carried out by taking real time data.

Comparative analysis of covering based soft rough sets and multi-layered fuzzy attributed fuzzy soft matrices

Comparative analysis of covering based soft rough sets and multi-layered fuzzy attributed fuzzy soft matrices

Soft rough sets based on covering and their applications

Soft rough based on covering SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document} theory has become a useful and well-known area of research in theories of uncertainty. The present work follows up on this flourishing research topic. We introduce a new model of SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document} in a fusion of soft set theory SST\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}ST$\\end{document} and rough set depending on covering CRS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {C}RS$\\end{document}. We put forth a definition of soft rough covering approximation space SCAS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}CAS$\\end{document} via neighborhood concept. Some axiomatic systems of our model of SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document} are discussed. We study the relationship between our model of SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document} and three other SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document}-models. An algorithm for reduction of the attributes of the information systems using SCAS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}CAS$\\end{document} is established. Based on the theoretical discussion, we set forth some applications of our model which will be helpful in decision making process via SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document} theory.

Soft rough fuzzy sets based on covering

<abstract><p>Soft rough fuzzy sets ($ \mathcal SRFSs $) represent a powerful paradigm that integrates soft computing, rough set theory, and fuzzy logic. This research aimed to comprehensively investigate the various dimensions of $ \mathcal SRFSs $ within the domain of approximation structures. The study encompassed a wide spectrum of concepts, ranging from covering approximation structures and soft rough coverings to soft neighborhoods, fuzzy covering approximation operators, and soft fuzzy covering approximation operators. We introduced three models of $ \mathcal SRFSs $ based on covering via the core of soft neighborhood. We discussed and analyzed our models' characteristics and properties. The relations between our models for soft fuzzy covering sets and Zhan's model for soft rough fuzzy covering were presented.</p></abstract>

New soft rough approximations via ideals and its applications

<abstract><p>Theories of soft sets and rough sets are two different approaches to analyzing vagueness. A possible fusion of rough sets and soft sets was proposed in 2011. At this time the concept of soft rough sets was introduced, where parametrized subsets of a universal set are basic building blocks for lower and upper approximations of a subset. The main purpose of soft rough sets is to reduce the soft boundary region by increasing the lower approximation and decreasing the upper approximation. In this paper, we present two new approaches for soft rough sets that is related to the notion of ideals. The main characteristics of these recent approaches are explained and interpreted through the use of suitable propositions and examples. These recent approaches satisfy most of the conditions of well known properties of Pawlak's model. Comparisons between our methods and previous ones are introduced. In addition, we prove that our approaches produce a smaller boundary region and greater value of accuracy than the corresponding defined definitions. Furthermore, two new styles of approximation spaces related to two distinct ideals, called soft bi-ideal approximation spaces, are introduced and studied. Analysis of the fulfilled and the non-fulfilled properties is presented, and many examples to ensure and explain the advantages and the disadvantages between our styles and the previous ones are provided.</p></abstract>

Increasing and Decreasing Soft Rough Set Approximations

Increasing and Decreasing Soft Rough Set Approximations

Retracted: On Three Types of Soft Rough Covering-Based Fuzzy Sets

Retracted: On Three Types of Soft Rough Covering-Based Fuzzy Sets

Study on Chaotic Multi-Attribute Group Decision Making Based on Weighted Neutrosophic Fuzzy Soft Rough Sets

In this article, we have proposed a multi-attribute group decision making (MAGDM) with a new scenario or new condition named Chaotic MAGDM, in which not only the weights of the decision makers (DMs) and the weights of the decision attributes are considered, but also the familiarity of the DMs with the attributes are considered. Then we applied the weighted neutrosophic fuzzy soft rough set theory to Chaotic MAGDM and proposed a new algorithm for MAGDM. Moreover, we provide a case study to demonstrate the application of the algorithm. Our contributions to the literature are as follows: (1) familiarity is rubbed into MAGDM for the first time in the context of neutrosophic fuzzy soft rough sets; (2) a new MAGDM model based on neutrosophic fuzzy soft rough sets has been designed; (3) a sorting/ranking algorithm based on a neutrosophic fuzzy soft rough set is constructed.

Dynamic Chaotic Multi-Attribute Group Decision Making under Weighted T-Spherical Fuzzy Soft Rough Sets

In this article, the parameter of the decision maker’s familiarity with the attributes of the alternatives is introduced for the first time in dynamic multi-attribute group decision making to avoid the disadvantages arising from the inappropriate grouping of decision makers. We combine it with fuzzy soft rough set theory and dynamic multi-attribute-grouping decision making to obtain a new decision model, i.e., dynamic chaotic multiple-attribute group decision making. Second, we provide an algorithm for solving this model under a weighted T-spherical fuzzy soft rough set, which can not only achieve symmetry between decision evaluation and fuzzy information but also establish a good symmetrical balance between decision makers and attributes (evaluation indexes). Finally, a specific numerical computation case is proposed to illustrate the convenience and effectiveness of our constructed algorithm. Our contributions to the literature are: (1) We introduced familiarity for the first time in dynamic multi-attribute group decision making. This makes our given dynamic chaotic multi-attribute group decision-making (DCMAGDM) model more general and closer to the actual situation; (2) we combined dynamic chaotic multi-attribute group decision making with T-spherical fuzzy soft rough set theory to make the model more realistic and reflect the actual situation. In addition, our choice of T-spherical fuzzy soft rough set allows the decision maker to engage in a sensible evaluation rather than sticking to numerical size choices; and (3) we constructed a new and more convenient sorting/ranking algorithm based on weighted T-spherical fuzzy soft rough sets.

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}) 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} say, varDelta -topological spaces (i.e., varDelta -TS). Hence, the topological properties for varDelta -TS models such as varDelta -open sets, varDelta -closed sets, varDelta -interior, varDelta -closure, varDelta -boundary, varDelta -neighborhood and varDelta -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.

A new approach to neutrosophic soft rough sets

A new approach to neutrosophic soft rough sets

Inverse Soft Rough Sets and Its Application in Decision Making

Inverse Soft Rough Sets and Its Application in Decision Making

Medical diagnosis for the problem of Chikungunya disease using soft rough sets

<abstract><p>One of the most difficulties that doctors face when diagnosing a disease is making an accurate decision to correctly determine the nature of the injury. This is attributable to the similarity of symptoms for different diseases. The current work is devoted to proposing new mathematical methodologies to help in precise decision-making in the medical diagnosis of the problem of Chikungunya virus disease through the use of soft rough sets. In fact, we introduce some improvements for soft rough sets (given by Feng et al.). We suggest a new approach to studying roughness through the use of soft sets to find approximations of any set, i.e., so-called "soft $ \delta $-rough sets". To illustrate this approach, we compare it with the previous studies and prove that the proposed approach is more accurate than the previous works. The proposed approach is more accurate than Feng et al. approach and extends the scope of applications because the problem of soft upper approximation is solved. The main characterizations of the presented technique are elucidated. Some important relations related to soft $ \delta $-rough approximations (such as soft $ \delta $-memberships, soft $ \delta $-equality and soft $ \delta $-inclusion) are provided and their properties are examined. In addition, an important medical application in the diagnosis of the problem of Chikungunya virus using soft $ \delta $-rough sets is provided with two algorithms. These algorithms were tested on fictitious data in order to compare them to existing methods which represent simple techniques to use in MATLAB. Additionally, we examine the benefits and weaknesses of the proposed approach and present a plan for some upcoming work.</p></abstract>

Different characterization of soft substructures in quantale modules dependent on soft relations and their approximations

<abstract> <p>The quantale module introduced by Abramsky and Vickers, engaged a large number of researchers. This research article focuses the combined behavior of rough set, soft set and an algebraic structure quantale module with the left action. In fact, the paper reflects the generalization of rough soft sets. This combined effect is totally dependent on soft binary relation including aftersets and foresets. Different soft substructures in quantale modules are defined. The characterizations of soft substructures in quantale modules based on soft binary relation are presented. Further, in quantale modules, we define soft compatible and soft complete relations in terms of aftersets and foresets. Furthermore, we use soft compatible and soft complete relations to approximate soft substructures of quantale modules and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough soft quantale modules. Additionally, we describe the algebraic relationships between the upper (lower) approximations of soft substructures of quantale modules and the upper (lower) approximations of their homomorphic images using the concept of soft quantale module homomorphism.</p> </abstract>

A new approach of soft rough sets and a medical application for the diagnosis of Coronavirus disease

<abstract><p>Rough set and soft set theories presents the mathematical foundations for studying decision making problems in different contexts. Some authors have established their own approaches regarding this theory, such as the "soft pre-rough approximation" and "soft $ \beta $-rough approaximation". In this study, the rationale and results of these two approaches were rigorously analyzed and it was concluded that they are the same. In addition, it was proven that some of the results established with the aforementioned approaches are not true, so we present two proposed modifications to the soft rough approximations, one of which represents an improvement in accuracy with respect to the exposed methods. The approaches addressed in this document were implemented to diagnose COVID-19 in a contextualized situation of a group of patients in Colombia, showing that our proposal obtained the highest accuracy. In addition, an algorithm was designed, which allows analyzing data with a larger universe and set of parameters than those presented in the theoretical and practical examples.</p></abstract>

Bipolar soft ideal rough set with applications in COVID-19

Bipolar soft rough set represents an important mathematical model to deal with uncertainty. This theory represents a link between bipolar soft set and rough set theories. This study introduced the concept of topological bipolar soft set by combining a bipolar soft set with topologies. Also, the topological structure of bipolar soft rough set has been discussed by defining the bipolar soft rough topology. The main objective of this paper is to present some solutions to develop and modify the approach of the bipolar soft rough sets. Two kinds of bipolar soft ideal approximation operators which represent extensions of bipolar soft rough approximation operator have been presented. Moreover, a new kind of bipolar approximation space via two ideals, called bipolar soft biideal approximation space, was introduced and studied by two different methods. Their properties are discussed and the relationships between these methods and the previous ones are proposed. The importance of these methods is reducing the vagueness of uncertainty areas by increasing the bipolar lower approximations and decreasing the bipolar upper approximations. Also, the bipolar soft biideal rough sets represent two opinions instead of one opinion. Finally, an application in multicriteria group decision making (MCGDM) in COVID-19 by using bipolar soft ideal rough sets is suggested by using two methods.

Novel Bipolar Soft Rough-Set Approximations and Their Application in Solving Decision-Making Problems

Novel Bipolar Soft Rough-Set Approximations and Their Application in Solving Decision-Making Problems

Decision-Making Framework Based on Multineutrosophic Soft Rough Sets

The uncertain data appear in majority of real-world phenomena regarding business, engineering, manufacturing, industries, medical, and other social fields. The neutrosophic sets (NSs), soft sets (SSs), and rough sets (RSs) are distinct mathematical models to deal with different types of uncertainties in data and information. Nowadays, several hybrid models are emerging as their combination or their further generalizations. In this paper, the concept of multineutrosophic fuzzy soft rough sets (MNFSRSs) by combining multineutrosophic fuzzy soft sets (MNSSs) with RSs is presented. Certain eminent features of the proposed structure are investigated. Moreover, a general decision-making (DM) algorithm is described for DM problems to indicate the effectiveness of the presented model.

Soft Rough Set based span for unsupervised keyword extraction

The present work proposes an application of Soft Rough Set and its span for unsupervised keyword extraction. In recent times Soft Rough Sets are being applied in various domains, though none of its applications are in the area of keyword extraction. On the other hand, the concept of Rough Set based span has been developed for improved efficiency in the domain of extractive text summarization. In this work we amalgamate these two techniques, called Soft Rough Set based Span (SRS), to provide an effective solution for keyword extraction from texts. The universe for Soft Rough Set is taken to be a collection of words from the input texts. SRS provides an ideal platform for identifying the set of keywords from the input text which cannot always be defined clearly and unambiguously. The proposed technique uses greedy algorithm for computing spanning sets. The experimental results suggest that extraction of keywords using the proposed scheme gives consistent results across different domains. Also, it has been found to be more efficient in comparison with several existing unsupervised techniques.