Rough Set Model Research Articles

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

In this paper, we generalize six kinds of rough set models based on j-neighborhood space (i.e., reflexive 1 j-neighborhood rough set, reflexive 2 j-neighborhood rough set, reflexive 3 j-neighborhood rough set, similarity 4 j-neighborhood rough set, similarity 5 j-neighborhood rough set, and similarity 6 j-neighborhood rough set) and investigate some of their basic properties. Further, we propose a new neighborhood space called j-adhesion neighborhood based on six types of rough set models (i.e., reflexive 7 j-adhesion neighborhood rough set, reflexive 8 j-adhesion neighborhood rough set, reflexive 9 j-adhesion neighborhood rough set, similarity 10 j-adhesion neighborhood rough set, similarity 11 j-adhesion neighborhood rough set, and similarity 12 j-neighborhood rough set) to reduce the boundary region and the accuracy. The fundamental properties of approximation operators based on j-adhesion neighborhood space are investigated. The relationship between the properties of these types is explained. Finally, we give comparisons between the proposed approach with the previous approach (i.e., Abo-Tabl’s approach and Dai et al.’s approach) from six types of rough set models. Consequently, the accuracy from the proposed approach is improved.

A novel approach to three-way conflict analysis and resolution with Pythagorean fuzzy information

As a universal phenomenon, conflicts exist widely in various walks of life, such as politics, economic lives, military operations, and cultural exchanges. In order to sove more complex and uncertain-conflict problems than what is possible within the confinement of current knowledge, this paper proposes a three-way conflict analysis model and conflict-degree based decision-theoretic rough set model for conflict resolution under Pythagorean fuzzy information. Firstly, we define a novel conflict distance and conflict function with Pythagorean fuzzy information from the perspective of absolute and relative conflict. We examine respectively a trisection of the conflict relation between a pair of agents, that among agents, that among disputes, and that among alliances. We also introduce the concepts of maximal strong alliances and maximal weak alliances. All of these efforts are then used to explain the reason for the emergence of conflicts. Secondly, to find an optimal feasible strategy for a given conflict situation, we propose a Pythagorean fuzzy decision-theoretic rough set model based on conflict functions and define the score function for each feasible strategy. Finally, for verifying our proposed model, a three-way conflict analysis and resolution are employed to address a governance issue of a local government.

A novel three-way decision approach in decision information systems

Given that the three-way decision (3WD) theory provides a scientific solution and reasonable semantic interpretation for solving multi-criteria decision-making (MCDM) problems, this paper presents a new 3WD model and applies it to realistic MCDM problems. Since the fuzzy neighborhood operator is effective in handling uncertain data, we first define a pair of probabilistic approximation operators via the constructed α-fuzzy neigh borhood class. Then, a 3WD model is explored in decision information systems to address the related issues in the proposed fuzzy probabilistic rough set model. In light of the above works, we establish a novel approach to classify and rank applicants for enterprise talent recruitment problems. Instead of the rule of tie-breaking, a way is given to separate applicants into three parts by combining decision attributes, and the feasibility of the approach is confirmed as well. Finally, by using a data set in the UCI database, the results of comparative and experimental analyses demonstrate that the constructed MCDM approach owns better performances in terms of effectiveness and stability.

Topologies Generated by Two Ideals and the Corresponding j -Approximations Spaces with Applications

Ideal is a fundamental concept in topological spaces and plays an important role in the study of topological problems. This motivated us to use two ideals to generate different topologies to take the advantage of the two ideals at the same time. Two ideals represent two opinions instead of one opinion which is very useful for using the insights of two groups of experts to study the problem and elicit decisions based on their common vision. Topology is a rich source for constructs that is helpful to enrich the original model of approximations spaces. Rough set theory has inbuilt topological concepts. Hence, the main purpose of this paper is to point out that the concept of rough sets has a purely topological aspects nature. To do so, new approximations spaces are introduced and defined based on the topologies generated by two ideals. The results in this paper show that the topological concepts can be a powerful method to study rough set models. The basic properties of these approximations are studied and compared to the previous ones and shown to be more general. The importance of the current paper is not only introducing a new kind of rough set based on bi-ideals, increasing the accuracy measure, and reducing the boundary region of the sets which is the main aim of rough set but also introducing a chemical application to explain the concepts.

An Efficient Model for the Approximation of Intuitionistic Fuzzy Sets in terms of Soft Relations with Applications in Decision Making

The basic notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation. This paper proposes an intuitionistic fuzzy rough set (IFRS) model which is a combination of intuitionistic fuzzy set (IFS) and rough set. We approximate an IFS by using soft binary relations instead of fixed binary relations. By using this technique, we get two pairs of intuitionistic fuzzy (IF) soft sets, called the upper approximation and lower approximation with respect to foresets and aftersets. Properties of newly defined rough set model (IFRS) are studied. Similarity relations between IFS with respect to this rough set model (IFRS) are also studied. Finally, an algorithm is constructed depending on these approximations of IFSs and score function for decision-making problems, although a method of decision-making algorithm has been introduced for fuzzy sets already. But, this new IFRS model is more accurate to solve the problem because IFS has degree of nonmembership and degree of hesitant.

Hierarchical sequential three-way decision model

Knowledge acquisition is one of the important issues in granular computing. In recent years, scholars have paid much attention to this problem and proposed the rule-based acquisition algorithms. However, a large number of the decision rules mined by the existing algorithms are not comprehensible. At the same time, the long detailed rules are easy to lead to over-fitting. In order to generate simpler and easier-to-comprehensible rules and improve human decision-making, a hierarchical sequential three-way decision model is proposed by combining sequential three-way decisions with hierarchical rough set model. Specifically, we generalize the concepts of the conditional attributes through the concept hierarchy tree, design the multi-hierarchical decision table with multiple levels of granularity, and illustrate the corresponding algorithm to acquire the generalized rules step by step. The experimental results demonstrate that the proposed model can mine hierarchical sequential three-way decision rules under different levels of granularity.

A formal study of a generalized rough set model based on subset approximation structure

This article presents a generalized rough set model based on a structure where we have a collection of subsets of the domain of discourse along with the accessibility relation. A modal logic for such a structure is proposed and the important properties of the logic viz. axiomatization, decidability, expressibility etc. are discussed.

Attribute‐scale selection for hybrid data with test cost constraint: The approach and uncertainty measures

Recently several novel cost-sensitive attribute-scale selection approaches have been proposed based on measurement errors. They are significant because they can simultaneously select attributes and scale combination to minimize the cost consumed in data processing. However, these approaches cannot deal with hybrid data with test cost constraint, and most of them do not consider the scale diversity between different attributes; and these approaches do not touch the uncertainty measurement, all of which are important issues in real applications. To address this situation, in this paper an effective cost-sensitive attribute-scale selection approach is presented based on the rough set theory, and multiple relevant uncertainty measures are developed. The main contributions of the paper are threefold. First, a generalized confidence level vector-based neighborhood rough set model is constructed. It takes into account the scale diversity between different attributes of hybrid data. Then, multiple uncertainty measures are developed. They consider both attributes and scales, thus are more general than existing ones which consider only attributes or only scales. Finally, an efficient heuristic attribute-scale selection algorithm is designed, which can select attributes and their respective scales to minimize the consumed total cost of hybrid data under any rational value of test cost upper bound. Detailed experiments thoroughly confirm the effectiveness of the proposed cost-sensitive attribute-scale selection approach. The experiments also reveal the influences of different test cost upper bounds to the attribute-scale selection and some related quantities including the uncertainty measures. This study would enrich the rough set theory to some extent, and provide an effective support for some test cost-constrained decision makings.

Two Different Views for Generalized Rough Sets with Applications

Rough set philosophy is a significant methodology in the knowledge discovery of databases. In the present paper, we suggest new sorts of rough set approximations using a multi-knowledge base; that is, a family of the finite number of general binary relations via different methods. The proposed methods depend basically on a new neighborhood (called basic-neighborhood). Generalized rough approximations (so-called, basic-approximations) represent a generalization to Pawlak’s rough sets and some of their extensions as confirming in the present paper. We prove that the accuracy of the suggested approximations is the best. Many comparisons between these approaches and the previous methods are introduced. The main goal of the suggested techniques was to study the multi-information systems in order to extend the application field of rough set models. Thus, two important real-life applications are discussed to illustrate the importance of these methods. We applied the introduced approximations in a set-valued ordered information system in order to be accurate tools for decision-making. To illustrate our methods, we applied them to find the key foods that are healthy in nutrition modeling, as well as in the medical field to make a good decision regarding the heart attacks problem.

A Dynamic Method Based-matrix for Batch Updating Decision Regions of Hybrid Information System

Dynamics and complexity are the important characteristics of current information systems, and intelligent decision-making problem of complex information systems in dynamic environment is an important research content in the fields of intelligent decision-making. Decision-theoretic rough set model is an important model based on rough computing, and matrix is an effective mathematical tool, which was widely used in various fields of intelligent computing because of its easy representation and convenient calculation. In this paper, neighbourhood decision-theoretic rough sets(NDTRS) and the dynamic updating methods of decision regions of hybrid decision information systems were studied, and a dynamic method based-matrix for batch updating decision regions of hybrid decision information systems was proposed by introducing neighbourhood relation matrix and probability matrix to calculate the decision regions.At the same time, In the process of algorithm design, the incremental matrix is defined to updated the probability matrix, so as to improve the algorithm from the perspective of time complexity.Furthermore,the algorithms were described and analyzed in detail.Finally, the experimental results fully proved the effectiveness and feasibility of the algorithm.

Different kinds of generalized rough sets based on neighborhoods with a medical application

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.

Some Topological Approaches for Generalized Rough Sets via Ideals

The idea of neighborhood systems is induced from the geometric idea of “near,” and it is primitive in the topological structures. Now, the idea of neighborhood systems has been extensively applied in rough set theory. The master contribution of this manuscript is to generate various topologies by means of the concepts of j -adhesion neighborhoods and ideals. Then, we define a new rough set model derived from these topologies and discussed main features. We show that these topologies are finer than those given in the previous ones under arbitrary binary relations. In addition, we elucidate that these topologies are finer than those topologies initiated based on different neighborhoods and ideals under reflexive relations. Several examples are provided to validate that our model is better than the previous ones.

Matrix‐based method for solving decision domains of neighbourhood multigranulation decision‐theoretic rough sets

It is more and more important to analyse and process complex data for gaining more valuable knowledge and making more accurate decisions. The multigranulation decision theory based on conditional probability and cost loss has the advantage of processing decision-making problems from multi-levels and multi-angles, and the neighbourhood rough set model (NRS) can facilitate the analysis and processing of numerical or mixed type data, and can address the limitation of multigranulation decision-theoretic rough sets (MG-DTRS), which is not easy to cope with complex data. Based on the in-depth study of hybrid-valued decision systems and MG-DTRS models, this study analysed neighbourhood MG-DTRS (NMG-DTRS) deeply by fusing MG-DTRS and NRS; a matrix-based approach for approximation sets of NMG-DTRS model was proposed on the basis of the matrix representations of concepts; the positive, boundary and negative domains were constructed from the matrix perspective, and the concept of positive decision recognition rate was introduced. Furthermore, the authors explored the related properties of NMG-DTRS model, and designed and described the corresponding solving algorithms in detail. Finally, some experimental results that were employed not only verified the effectiveness and feasibility of the proposed algorithm, but also showed the relationship between the decision recognition rate and the granularity and threshold.

Three‐way decisions based on some Hamacher aggregation operators under double hierarchy linguistic environment

This paper proposes an approach to linguistic three-way decision making problem with double hierarchy linguistic term evaluation information. Double hierarchy linguistic term set consists of the first hierarchy and second hierarchy linguistic term set, which can describe uncertainty and fuzziness more flexibly. First, the Hamacher operational rules, score function and distance measure of double hierarchy linguistic elements are defined. Next, we construct the double hierarchy linguistic decision-theoretic rough set model. And the conditional probability is calculated based on the double hierarchy linguistic term environment with grey relational analysis, which makes the process of decisions more rational. Then the loss functions are aggregated by the double hierarchy linguistic Hamacher weighted averaging operator, which takes into account different decision attitudes of decision makers. And the results of decision are deduced by the minimum-loss principle. Finally, a case study about the selection of cooperation companies during the COVID-19 is used to demonstrate the practicability of our proposed method.

Intuitionistic Fuzzy (IF) Overlap Functions and IF-Rough Sets with Applications

Overlap function (which has symmetry and continuity) is widely used in image processing, data classification, and multi-attribute decision making problems. In recent years, theoretical research on overlap function has been extended to interval valued overlap function and lattice valued overlap function, but intuitionistic fuzzy overlap function (IF-overlap function) has not been studied. In this paper, the concept of IF-overlap function is proposed for the first time, then the generating method of IF-overlap function is given. The representable IF-overlap function is defined, and the concrete examples of representable and unrepresentable IF-overlap functions are given. Moreover, a new class of intuitionistic fuzzy rough set (IF-roght set) model is proposed by using IF-overlap function and its residual implication, which extends the IF-rough set model based on intuitionistic fuzzy triangular norm, and the basic properties of the new intuitionistic fuzzy upper and lower approximate operators are analyzed and studied. At the same time, the established IF-rough set based on IF-overlap function is applied to MCDM (multi-criteria decision-making) problems, the intuitionistic fuzzy TOPSIS method is improved. Through the comparative analysis of some cases, the new method is proved to be flexible and effective.

Spherical Linear Diophantine Fuzzy Soft Rough Sets with Multi-Criteria Decision Making

Modeling uncertainties with spherical linear Diophantine fuzzy sets (SLDFSs) is a robust approach towards engineering, information management, medicine, multi-criteria decision-making (MCDM) applications. The existing concepts of neutrosophic sets (NSs), picture fuzzy sets (PFSs), and spherical fuzzy sets (SFSs) are strong models for MCDM. Nevertheless, these models have certain limitations for three indexes, satisfaction (membership), dissatisfaction (non-membership), refusal/abstain (indeterminacy) grades. A SLDFS with the use of reference parameters becomes an advanced approach to deal with uncertainties in MCDM and to remove strict limitations of above grades. In this approach the decision makers (DMs) have the freedom for the selection of above three indexes in [0,1]. The addition of reference parameters with three index/grades is a more effective approach to analyze DMs opinion. We discuss the concept of spherical linear Diophantine fuzzy numbers (SLDFNs) and certain properties of SLDFSs and SLDFNs. These concepts are illustrated by examples and graphical representation. Some score functions for comparison of LDFNs are developed. We introduce the novel concepts of spherical linear Diophantine fuzzy soft rough set (SLDFSRS) and spherical linear Diophantine fuzzy soft approximation space. The proposed model of SLDFSRS is a robust hybrid model of SLDFS, soft set, and rough set. We develop new algorithms for MCDM of suitable clean energy technology. We use the concepts of score functions, reduct, and core for the optimal decision. A brief comparative analysis of the proposed approach with some existing techniques is established to indicate the validity, flexibility, and superiority of the suggested MCDM approach.

Forecasting of Indian Stock Market Using Rough Set and Fuzzy-Rough Set Based Models

ABSTRACT Rough Set models are being practiced for several decades for dealing with vagueness and uncertainty in data. The present paper explores its applicability in forecasting future stock market prices of Indian companies. In this work, Rough Set and Fuzzy-Rough Set are used as feature selection techniques in conjunction with CN2 algorithm for the generation of rules for future price prediction. Prediction in the present model is in the form of trinary classification, namely it will increase or decrease or will undergo marginal change. Our experiments suggest that the proposed technique performs significantly better than several popular classification algorithms, namely, Support Vector Machines, Random Forest, Artificial Neural Networks, Gaussian Naïve Bayes and ARIMA.

The study on the anxiety level of college students in emergencies based on fuzzy rough set over two universes

In 2020, the spread of the COVID-19 epidemic has attracted global attention. As a large-scale group that is receiving higher education, college students also show greater mood swings. How to reduce the psychological harm of anxiety to college students is a problem that needs to be solved urgently. Based on this, this paper proposes an evaluation model for the anxiety level of college students in different regions under the influence of COVID-19. First of all, the general influence index of college student’s anxiety level is obtained by correlation analysis. Secondly, the logical OR of the double quantization variable precision fuzzy set model and the degree fuzzy rough set model is used to establish the evaluation model of the anxiety level of college students under the influence of COVID-19. Finally, used big data, the idea of fuzzy upper and lower approximation, combined with the principle of maximum membership in fuzzy set theory, achieved the quantitative ranking of the anxiety levels of college students in different areas. The research shows that when the accuracy of decision-making is 45%, the anxiety level of the township college students group and the provincial capital or municipality college students group is higher. When the accuracy of decision-making is 65%, the anxiety level of the provincial capital or municipality college students group is higher than others.

(α, β)-Multi-granulation bipolar fuzzified rough sets and their applications to multi criteria group decision making

Pawlak’s rough set theory based on single granulation has been extended to multi-granulation rough set structure in recent years. Multi-granulation rough set theory has become a flouring research direction in rough set theory. In this paper, we propose the notion of (α, β)-multi-granulation bipolar fuzzified rough set ((α, β)-MGBFRSs). For this purpose, a collection of bipolar fuzzy tolerance relations has been used. In the framework of multi-granulation, we proposed two types of (α, β)-multi-granulation bipolar fuzzified rough sets model. One is called the optimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) o-MGBFRSs) and the other is called the pessimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) p-MGBFRSs). Subsequently, a number of important structural properties and results of proposed models are investigated in detail. The relationships among the (α, β)-MGBFRSs, (α, β) o-MGBFRSs and (α, β) p-MGBFRSs are also established. In order to illustrate our proposed models, some examples are considered, which are helpful for applying this theory in practical issues. Moreover, several important measures associated with (α, β)-multi-granulation bipolar fuzzified rough set like the measure of accuracy, the measure of precision, and accuracy of approximation are presented. Finally, we construct a new approach to multi-criteria group decision-making method based on (α, β)-MGBFRSs, and the validity of this technique is illustrated by a practical application. Compared with the existing results, we also expound its advantages.

An approach to MCGDM based on multi-granulation Pythagorean fuzzy rough set over two universes and its application to medical decision problem.

Exploring efficiency approaches to solve the problems of decision making under uncertainty is a mainstream direction. This article explores the rough approximation of the uncertainty information with Pythagorean fuzzy information on multi-granularity space over two universes combined with grey relational analysis. Based on grey relational analysis, we present a new approach to calculate the relative degree or the attribute weight with Pythagorean fuzzy set and give a new descriptions for membership degree and non-membership. Then, this paper proposes a multi-granulation rough sets combined with Pythagorean fuzzy set, including optimistic multi-granulation Pythagorean fuzzy rough set, pessimistic multi-granulation Pythagorean fuzzy rough set and variable precision Pythagorean fuzzy rough set. Several basic properties for the established models are investigated in detail. Meanwhile, we present an approach to solving the multiple-criteria group decision making problems with fuzzy information based on the proposed model. Eventually, a case study of psychological evaluation of health care workers in COVID-19 show the principle of the established model and is utilized to verify the availability. The main contributions have three aspects. The first contribution of an approach of calculating the attribute weight is presented based on Grey Relational Analysis and gives a new perspective for the Pythagorean fuzzy set. Then, this paper proposes a mutli-granulation rough set model with Pythagorean fuzzy set over two universes. Finally, we apply the proposed model to solving the psychological evaluation problems.