Rough Set Model Research Articles

Topological Characterizations of Rough Set Theory Based on Quantum Logic

Rough set theory is a mathematical approach for dealing with uncertain and imperfect knowledge processing. This paper investigates rough sets based on quantum logic, i.e., orthomodular lattice-valued logic. Some properties of the lower and upper approximations are proposed. Finally, some topological characterizations of the new rough set model are discussed.

Multi‐granularity decision rough set attribute reduction algorithm under quantum particle swarm optimization

The existing attribute reductions are carried out using equivalence relations under a complete information system, and there is less research on attribute reductions of incomplete information systems with new theoretical models such as multi-granularity decision rough sets. To address the above shortcomings, this paper first makes up a pessimistic-optimistic multi-granularity decision rough set model based on tolerance relations in incomplete information systems. The concepts of attribute importance and approximate distribution quality are introduced into the model to form an attribute reduction algorithm under incomplete information systems. Secondly, due to the NP-hard problem of attribute reduction, in order to further ensure the accuracy of the reduction result, this paper proposes a pessimistic-optimistic multi-granularity reduction algorithm under quantum particle swarm optimization. Experimental results on multiple-attribute data proved that the algorithm proposed in this paper can effectively attribute reduction in the decision table with missing data. At the same time, the algorithm of this paper has the role of iterative optimization search, ensuring the accuracy of the reduction results and increasing the applicability of multi-granularity decision rough sets.

Pessimistic Multigranulation Rough Set of Intuitionistic Fuzzy Sets Based on Soft Relations

Qian presented multigranulation rough set (MGRS) models based on Pawlak’s rough set (RS) model. There are two types of MGRS models, named optimistic MGRS and pessimistic MGRS. Recently, Shabir et al. presented an optimistic multigranulation intuitionistic fuzzy rough set (OMGIFRS) based on soft binary relations. This paper explores the pessimistic multigranulation intuitionistic fuzzy rough set (PMGIFRS) based on soft relations combined with a soft set (SS) over two universes. The resulting two sets are lower approximations and upper approximations with respect to the aftersets and foresets. Some basic properties of this established model are studied. Similarly, the MGRS of an IFS based on multiple soft relations is presented and some algebraic properties are discussed. Finally, an example is presented that illustrates the importance of the proposed decision-making algorithm.

Pessimistic Multigranulation Roughness of a Fuzzy Set Based on Soft Binary Relations over Dual Universes and Its Application

The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes. Firstly, we approximate fuzzy set w.r.t aftersets and foresets of the finite number of soft binary relations. As a result, we obtained two sets of fuzzy soft sets known as the pessimistic lower approximation of a fuzzy set and the pessimistic upper approximation of a fuzzy set—the w.r.t aftersets and the w.r.t foresets. The pessimistic lower and pessimistic upper approximations of the newly proposed multigranulation rough set model are then investigated for several interesting properties. This article also addresses accuracy measures and measures of roughness. Finally, we give a decision-making algorithm as well as examples from the perspective of application.

On (O,G)-fuzzy rough sets based on overlap and grouping functions over complete lattices

In rough set theory, upper and lower approximation operators are two crucial concepts. The study of these two approximation operators in the framework of lattice theory is an important generalization from the mathematical point of view. On the other hand, overlap and grouping functions, as two types of not necessarily associative binary aggregation functions different from the common binary aggregation functions triangular norms and triangular conorms, have not only rich theoretical results but also a wide range of practical applications. Therefore, based on overlap and grouping functions over complete lattices, this paper is devoted to proposing (O,G)-fuzzy rough sets as a further generalization of the notion of rough sets. Firstly, we define a pair of O-upper and G-lower L-fuzzy rough approximation operators and investigate basic properties of them. Then, the characterizations of (O,G)-fuzzy rough approximation operators are discussed by using different kinds of L-fuzzy relations. Meanwhile, we investigate the topological properties of (O,G)-fuzzy rough sets. Furthermore, we show a brief comparison of the (O,G)-fuzzy rough sets with other common rough set models. At the end of this paper, we further propose multigranulation (O,G)-fuzzy rough sets over complete lattices from the viewpoint of multigranulation structure.

A novel method to attribute reduction based on weighted neighborhood probabilistic rough sets

Attribute reduction is an important application of rough set theory. Most existing rough set models do not consider the weight information of attributes in information systems. In this paper, we first study the weight of each attribute in information systems by using data binning method and information entropy theory. Then, we propose a new rough set model of weighted neighborhood probabilistic rough sets (WNPRSs) and investigate its basic properties. Meanwhile, the dependency degree formula of an attribute relative to an attribute subset is defined based on WNPRSs. Subsequently, we design a novel attribute reduction method by using WNPRSs and the corresponding algorithm is also given. Finally, to evaluate the performance of the proposed algorithm, we conduct a data experiment and compare it with other existing attribute reduction algorithms on eight public datasets. Experimental result demonstrates that the proposed attribute reduction algorithm is effective and performs better than some of the existing algorithms.

Generalized neighborhood systems-based pessimistic rough sets and their applications in incomplete information systems

In this paper, we point out that Lin’s general neighborhood systems-based rough set model is an extension of Qian’s optimistic rough set model, and thus called optimistic general neighborhood systmes-based rough set model. Then we present a new rough set model based on general neighborhood systems, and prove that it is an extension of Qian’s pessimistic rough set model. Later, we study the basic properties of the proposed pessimistic rough sets, and define the serial, reflexive, symmetric, transitive and Euclidean conditions for general neighborhood systems, and explore the further properties of related rough sets. Furthermore, we apply the pessimistic general neighborhood systems-based rough set model in the research of incomplete information system, and build a three-way decision model based on it. A simple practical example to show the effectiveness of our model is also presented.

VIKOR method for MCDM based on bipolar fuzzy soft β-covering based bipolar fuzzy rough set model and its application to site selection of solar power plant

Bipolarity indicates the positive and negative aspects of a particular problem. The concept behind the bipolarity is that a huge range of human decision analysis is involved in bipolar subjective thoughts. The VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje) which means multicriteria optimization and compromise solution, has already become a quite popular multi-criteria decision making tool for its computational simplicity and solution accuracy. In this article, we propose a hybrid model for multi-criteria decision-making (MCDM) based on bipolar fuzzy soft β-covering based bipolar fuzzy rough sets using VIKOR technique. It consists of a suitable redesign of the VIKOR approach so that it can use information with bipolar configurations. This method focuses on selecting and ranking from a set of feasible alternatives, and determines compromise solution for a problem with conflicting criteria to help the decision maker in reaching a final course of action. It determines the compromise ranking list based on the particular measure of closeness to the ideal solution. For illustration, the proposed technique is applied to a decision-making problems, namely, the selection of site for renewable energy project (solar power plant). A comparison of this method with another aggregation operator method and with the existing decision making algorithm Fuzzy VIKOR is also presented.

Text Data Processing and Classification Algorithm Based on Data Fusion and Granular Computing

With the rapid expansion of network information and the emergence of a large number of electronic texts, how to organize and manage this massive information has become a major challenge. Automatic text categorization technology is to study how to let the machine classify unknown text through self-learning, thus solving the difficulties encountered in manual classification. Because granular computing can reduce the knowledge in solving complex problems, it is more convenient to summarize and acquire knowledge. It has become a hotspot in recent years, and it also provides new ideas for text classification research. The rough set model of granular computing can acquire knowledge by mining decision rules. The decision process is more transparent and easy to understand. It has been paid attention to and applied in text classification research. Based on the research of existing achievements, this paper makes a further study on the application of granular computing in text categorization. After analyzing the existing feature selection methods, the feature distribution is proposed based on the relationship between feature words and categories. By calculating the distribution distance between any two feature words, the feature words with similar distribution distances are aggregated, which effectively reduces the dimension of the feature space and also avoids the individual samples caused by the existing feature selection algorithm. A phenomenon that is discarded due to features. The experimental results show that the clustering method can obtain higher classification accuracy than other feature selection methods when using SVM as the classifier. SVM performs best, and the final text classification accuracy rate can reach 85.46%. According to the correlation principle of the rough set, feature selection is made for each information granularity, the selected feature is used as the condition attribute and the coordination matrix is constructed, and the most similar sample is heuristically searched to obtain the attribute reduction set.

Fuzzy covering-based rough set on two different universes and its application

In this paper, we propose a new type of fuzzy covering-based rough set model over two different universes by using Zadeh’s extension principle. We mainly address the following issues in this paper. First, we present the definition of fuzzy \(\beta\)-neighborhood, which can be seen as a fuzzy mapping from a universe to the set of fuzzy sets on another universe and study its properties. Then we define a new type of fuzzy covering-based rough set model on two different universes and investigate the properties of this model. Meanwhile, we give a necessary and sufficient condition under which two fuzzy \(\beta\)-coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Moreover, matrix representations of the fuzzy covering lower and fuzzy covering upper approximation operators are investigated. Finally, we propose a new approach to a kind of multiple criteria decision making problem based on fuzzy covering-based rough set model over two universes. The proposed models not only enrich the theory of fuzzy covering-based rough set but also provide a new perspective for multiple criteria decision making with uncertainty.

Hybrid filter–wrapper attribute selection with alpha-level fuzzy rough sets

Selection of important attributes/features from decision information systems plays a vital role in data mining and machine learning tasks. It is regarded as a very interesting, but challenge problem, especially when faced with continuous numerical/real attributes. Neighborhood rough sets and fuzzy rough sets based attribute selection methods are well-known for dealing effectively with numerical/real attributes. However, characteristics of data may be described incompletely by neighborhood classes in the neighborhood rough set model, while the fuzzy rough sets based approach is still quite time-consuming because of the complex calculations on fuzzy equivalence classes. To address these limitations, we apply the concept of sets of level α (α-cut sets) in the fuzzy set theory to construct α-level fuzzy equivalence classes which provide a foundation for developing basic concepts of a new α-level fuzzy rough set model. We will see that under the properties of the α-cut sets, the α-level fuzzy equivalence classes not only help to significantly reduce the computational cost, but also preserve most of the information about the relationships between the objects, and even can decrease some noise in the data. Based on the α-level fuzzy rough set model, we define new reducts and then propose the FSFCF algorithm for attribute subset selection from the decision information systems containing continuous data. It is important to emphasize some advantages of the proposed method. First, in order to evaluate and select optimal attributes, we use an α-level fuzzy certainty factor with the comprehensive consideration to all objects in the universe. Second, the FSFCF algorithm is designed in the hybrid filter–wrapper approach to reduce the size of selected attribute subset as well as enhance the classification accuracy. Therefore, the proposed method can significantly improve the performance of the attribute selection for continuous data. To verify the effectiveness of FSFCF, we implement experiments on a variety of real-world data sets. The results demonstrated that the proposed method outperforms the compared state-of-the-art methods in terms of the computational time, the size of reduct and the classification accuracy for almost all of data sets.

Multi-label feature selection based on fuzzy neighborhood rough sets

Multi-label feature selection, a crucial preprocessing step for multi-label classification, has been widely applied to data mining, artificial intelligence and other fields. However, most of the existing multi-label feature selection methods for dealing with mixed data have the following problems: (1) These methods rarely consider the importance of features from multiple perspectives, which analyzes features not comprehensive enough. (2) These methods select feature subsets according to the positive region, while ignoring the uncertainty implied by the upper approximation. To address these problems, a multi-label feature selection method based on fuzzy neighborhood rough set is developed in this article. First, the fuzzy neighborhood approximation accuracy and fuzzy decision are defined in the fuzzy neighborhood rough set model, and a new multi-label fuzzy neighborhood conditional entropy is designed. Second, a mixed measure is proposed by combining the fuzzy neighborhood conditional entropy from information view with the approximate accuracy of fuzzy neighborhood from algebra view, to evaluate the importance of features from different views. Finally, a forward multi-label feature selection algorithm is proposed for removing redundant features and decrease the complexity of multi-label classification. The experimental results illustrate the validity and stability of the proposed algorithm in multi-label fuzzy neighborhood decision systems, when compared with related methods on ten multi-label datasets.

Neighborhood Rough Set Approach With Biometric Application

This paper provides a new approach for human identification based on Neighborhood Rough Set (NRS) algorithm with biometric application of ear recognition. The traditional rough set model can just be used to evaluate categorical features. The neighborhood model is used to evaluate both numerical and categorical features by assigning different thresholds for different classes of features. The feature vectors are obtained from ear image and ear matching process is performed. Actually, matching is a process of ear identification. The extracted features are matched with classes of ear images enrolled in the database. NRS algorithm is developed in this work for feature matching. A set of 20 persons are used for experimental analysis and each person is having six images. The experimental result illustrates the high accuracy of NRS approach when compared to other existing techniques.

The Influence Factor Analysis of Symmetrical Half-Bridge Power Converter through Regression, Rough Set and GM(1,N) Model

Analysis of power converter performance has tended to be engineering-oriented, focusing mainly on voltage stability, output power and efficiency improvement. However, there has been little discussion about the weight relations between these factors. In view of the previous inadequacy, this study employs regression, rough set and GM(1,N) to analyze the relations among the factors that affect the converter, with a symmetrical half-bridge power converter serving as an example. The four related affecting factors, including the current conversion ratio, voltage conversion ratio, power conversion ratio and output efficiency, are firstly analyzed and calculated. The respective relative relations between output efficiency and the other three factors are obtained. This research can be referred to by engineers in their design of symmetrical half-bridge power converters.

Uncertainty Measurement and Attribute Reduction Algorithm Based on Kernel Similarity Rough Set Model

Attribute reduction is the core research content in rough set theory. At present, the attribute reduction of numerical information system mostly adopts the neighborhood rough set method. In order to further improve the similarity measurement effect between data objects, kernel function method is used to construct a new rough set model in numerical information system, and an uncertainty measurement method and attribute reduction method are proposed. Firstly, the similarity between objects of numerical information system is calculated by kernel function, and a granular structure model and rough set model based on kernel similarity relation are proposed. Then, from the perspective of kernel similarity rough approximation, an information system uncertainty measurement method called kernel approximation precision and kernel approximation roughness is proposed. Because these two measurement methods do not meet the strict monotonicity of information granulation, the concept of kernel knowledge granularity based on kernel similarity granular structure is further proposed in this paper. By combining kernel approximation precision and kernel approximation roughness with kernel knowledge granularity, an uncertainty measurement method of kernel similarity combination measurement is proposed. Finally, using the strict monotonicity of kernel similarity combination measurement, an attribute reduction algorithm for numerical information system is designed. Experimental analysis shows the effectiveness and superiority of the proposed method.

Rough set models in a more general manner with applications

<abstract><p>Several tools have been put forth to handle the problem of uncertain knowledge. Pawlak (1982) initiated the concept of rough set theory, which is a completely new tool for solving imprecision and vagueness (uncertainty). The main notions in this theory are the upper and lower approximations. One of the most important aims of this theory is to reduce the vagueness of a concept to uncertainty areas at their borders by decreasing the upper approximations and increasing the lower approximations. So, the object of this study is to propose four types of approximation spaces in rough set theory utilizing ideals and a new type of neighborhoods called "the intersection of maximal right and left neighborhoods". We investigate the master properties of the proposed approximation spaces and demonstrate that these spaces reduce boundary regions and improve accuracy measures. A comparative study of the present methods and the previous ones is given and shown that the current study is more general and accurate. The importance of the current paper is not only that it is introducing new kinds of approximation spaces relying mainly on ideals and a new type of neighborhoods which increases the accuracy measure and reduces the boundary region of subsets, but also that these approximation spaces are monotonic, which means that it can be successfully used to evaluate the uncertainty in the data. In the end of this paper, we provide a medical example of the heart attacks problem to show the efficiency of the current techniques in terms of approximation operators, accuracy measures, and monotonic property.</p></abstract>

Rough Approximation Spaces via Maximal Union Neighborhoods and Ideals with a Medical Application

One of the most popular and important tools to deal with imperfect knowledge is the rough set theory. It starts from dividing the universe to obtain blocks utilizing an equivalence relation. To make it more flexibility and expand its scope of applications, many generalized rough set models have been proposed and studied. To contribute to this area, we introduce new generalized rough set models inspired by “maximal union neighborhoods and ideals.” These models are created with the aim to help decision‐makers to analysis and evaluate the given data more accurately by decreasing the ambiguity regions. We confirm this aim by illustrating that the current models improve the approximations operators (lower and upper) and accuracy measures more than some existing method approaches. We point out that almost all major properties with respect to rough set model can be kept using the current models. One of the interesting obtained characterizations of the current models is preserving the monotonic property, which enables us to evaluate the vagueness in the data and enhance the confidence in the outcomes. Moreover, we compare the current approximation spaces with the help of concrete examples. Finally, we show the performance of the current models to discuss the information system of dengue fever disease and eliminate the ambiguity of the medical diagnosis, which produces an accurate decision.

Uncertainty Measure for Multisource Intuitionistic Fuzzy Information System

Multisource information systems and multigranulation intuitionistic fuzzy rough sets are important extended types of Pawlak’s classical rough set model. Multigranulation intuitionistic fuzzy rough sets have been investigated in depth in recent years. However, few studies have considered this combination of multisource information systems and intuitionistic fuzzy rough sets. In this paper, we give the uncertainty measure for multisource intuitionistic fuzzy information system. Against the background of multisource intuitionistic fuzzy information system, each information source is regarded as a granularity level. Considering the different importance of information sources, we assign different weights to them. Firstly, the paper proposes an optimal source selection method. Secondly, we study the weighted generalized, weighted optimistic, and weighted pessimistic multigranularity intuitionistic fuzzy rough set models and uncertainty measurement methods in the multisource intuitionistic fuzzy information system, and we further study the relationship between the three models and related properties. Finally, an example is given to verify the validity of the models and methods.

A Study on Soft Multi-Granulation Rough Sets and Their Applications

Rough set (RS) and soft set (SS) theories are two successful mathematical approaches to dealing with uncertainty in data analysis. The classical soft rough set (SRS) theory proposed by Feng et al. [8] offers a formal theoretical framework for solving the uncertainty under a single granulation environment. However, it is essential to note that the SRS theory cannot be applied in the context of multi-granulation in the real world. To address this issue, in this paper, we introduce the idea of soft multi-granulation RS (SMGRS) model based on two soft binary relations (S-BRs). Axiomatic operations, lower soft rough approximation space (lower SRA-space) and upper soft rough approximation space (upper SRA-space), are defined through after sets of soft relations. After that, the concept of SMGRSs is applied to a significant part of commutative algebra, group theory. In this respect, the primitive notions of SRA-spaces are defined with the help of two normal soft groups (NSGs). In groups, several important structural properties related to SMGRS are investigated in detail with illustrative examples. It is shown that SMGRS in groups may be influential in decision-making (DM) by some numerical examples. To demonstrate the flexibility, superiority, and effectiveness of the suggested technique, some comparative examples are given with some existing methods.

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.