Generalization Of Rough Sets Research Articles

Near open generalizations of rough sets and their applications

BackgroundThe concept of near open sets is a potent tool that empowers researchers to achieve a more encompassing approximation of rough sets, thereby enhancing the accuracy of measurements. The evolution of rough set theory into various generalized forms, based on topological structures, has emerged as a significant approach in the realm of knowledge discovery within databases.ResultsThis paper’s primary contribution lies in the introduction of a novel category of generalized near open sets, termed “inverse simply open sets,” within the context of the j\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{j}$$\\end{document}-neighborhood space. The paper proposes diverse methods for extending the Pawlak’s rough approximations leading to the definition of new approximations in the j\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{j}$$\\end{document}-neighborhood space. By employing these newly introduced generalizations, we establish fresh connections between two pivotal theories, namely “general topology and rough set theory”. Through a comprehensive investigation, we conduct multiple comparisons between our methodology and classical approaches. Furthermore, we showcase practical applications of these techniques within real-life scenarios, demonstrating their utility in decision-making processes.ConclusionsWe reduced the data’s ambiguity while increasing its accuracy measure. As a result, we may conclude that the proposed approximations were more precise than earlier techniques and contributed to the elimination of data ambiguity in real-world scenarios requiring accurate decisions.

Consistent Matrix: A Feature Selection Framework for Large-Scale Datasets

Large-scale data processing based on limited computing resources has always been a difficult problem in data mining, where feature selection is often used as an effective data compressing mechanism. For granular computing of big data, discernibility matrix and dependency degree are the most representative methods for matrix-based and feature importance degree-based feature selection, respectively. However, their temporal and space complexities are high and often lead to poor performance. In this paper, a novel feature selection framework for large scale data processing with linear complexities was proposed for the first time. Firstly, a much more concise fuzzy granule set, called fuzzy arithmetic covering, was introduced to reduce computational costs. Then a new matrix-based feature selection framework, namely consistent matrix, was proposed for general rough set models. As a result, a heuristic attribute reduction algorithm, i.e., HARCM, was designed accordingly. Compared with six state-of-the-art algorithms for feature selection, the average running time of the newly proposed algorithm was reduced up to 2913 times, with a comparable or even better classification performance.

On some generalization of rough sets

A new model of extended Rough Sets is provided. The model uses the concept of a generalized algebraic closure as a base for upper approximation and the concept of a generalized algebraic kernel as a base for lower approximation. Optimal approximations are also discussed. The extensions include multiple lower and upper approximations, optimal approximations, approximations satisfying very specific proprieties, and compositions of approximations.

Theoretical Innovation of English Teaching Methodology Based on Continuous Discretization Method

Abstract In the new era, English teaching methods urgently need to be innovated to meet modernization needs. In this paper, we study English teaching based on the continuous discretization method, build a framework of discretization process based on the theoretical foundation of discretization, implement continuous attribute discretization using the rough set method according to the characteristics of English teaching data, and further reduce the classification error by using variable precision rough set to address the limitations of the general rough set. Then, the continuous discretization method based on variable-precision rough sets is used to study the key influencing factors of English teaching outcomes and propose targeted innovative teaching methods. In teaching practice, students’ listening ability improved by 15.77%, and speaking ability improved by 15.13% under the innovative teaching method. Reading ability increased by 11.34%, and writing ability increased by 11.86%. This research method can optimize the English teaching evaluation method, build a higher quality English classroom for students, ensure the overall development of students’ English literacy and comprehensive quality, and effectively improve students’ overall English ability.

Approximate reasoning and the ethnomathematics of cooking

Several methods of approximate reasoning are known, and many remain to be discovered across domains. Some are tied to reasoning with uncertainty. The developments over the last fifty years or so in the development of approximate reasoning methods, and their application across multiple STEM domains, suggest that it is necessary to introduce them early in school. Whileefforts towards building the infrastructure for the process have been limited, the bigger question is “What should be introduced?”. If concepts are always approximated in real life, then how should they be done mathematically? If thereal numbers are not always necessary to approximate concepts or even quantities, then how should they be approximated, and what should be taught in schools? Specifically, functional representations of approximate reasoning are notintroduced early. This additionally impedes diversity, ethnomathematical explorations, learning from experience, and through models. The objective of this research is to explain the problem with a focus on the ethnomathematics of cooking, and associated haptic methods. Further, it is argued through the context that of the many approaches to approximate reasoning, intrusive methods are best avoided, and that general rough sets is better suited for modeling such knowledge. Intrusive methods, such as those based on fuzzy or probability theory, are those that indulge in an excess of unjustified numeric assumptions. This builds on earlier work of the present author on modeling approximate reasoning. Her axiomatic approach to granularity are additionally applicable to approximate recipes that possess desired properties. In the contexts of ethnomathematical discourse involving haptic reasoning (as in cooking), it is shown that such an approach can model the essence of context without oversimplifications or outright dismissal of the efforts involved. Further, it has the potential to help in inventing expressive structured languages for the ethnomathematics, and associated model eliciting activities. Distinct facets of three specific contexts are theoretically explored to illustrate aspects of the reasoning, and meta aspects.

General assembly framework for online streaming feature selection via Rough Set models

We may not know the entire feature space in advance for real-world applications, and features can exist in a stream mode, called streaming features. Online streaming feature selection aims to select optimal streaming features on the fly and can be summarized into three main components: irrelevant feature discarding, relevant feature selecting, and redundant feature removing. Therefore, the core issue of the streaming feature selection framework is the calculation of the relationship between features. This paper applies Rough Set models to discover the feature relationships for the most crucial advantages: they do not require any domain knowledge and can measure the selected features as integral. After the formal definitions of feature relevance, irrelevance, and redundancy from the Rough Set perspective, we analyze and abstract the feature relationship calculation from three levels: Rough Set model, positive region, and consistency calculation. Then we design a novel general assembly Rough Set based Streaming Feature Selection Framework, named RS-SFSF, which could assemble new algorithms for different problems step by step. Researchers in different areas can quickly build the algorithms they need based on our new framework. To demonstrate the effectiveness of RS-SFSF, we derived four new algorithms based on RS-SFSF by using the classical Rough Set model, neighborhood Rough Set model, and fuzzy Rough Set model, respectively. Extensive experiments conducted on twelve real-world datasets indicate the efficiency of our new framework.

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.

Generalization of rough sets using maximal right neighborhood systems and ideals with medical applications

<abstract><p>Rough set theory is a mathematical technique to address the issues of uncertainty and vagueness in knowledge. An ideal is considered to be a crucial extension of this theory. It is an efficacious tool to dispose of vagueness and uncertainties by helping us to approximate the rough set in a more general manner. Minimizing the boundary region is one of the pivotal and substantial themes for studying the rough sets which consequently aim to maximize the accuracy measure. An ideal is one of the effective and successful followed methods to achieve this goal perfectly. So, the objective of this work is to present new methods for rough sets by using ideals. Some important characteristics of these methods are scrutinized and demonstrated to show that they yield accuracy measures greater and higher than the former ones in the other approaches. Finally, two medical applications are introduced to show the significance of utilizing the ideals in the proposed methods.</p></abstract>

Generalizations of rough sets via topology

In this paper, we present a general framework for the study of rough sets using topological approaches. First, we introduce several concepts and properties of $$\tau -R$$ -open sets. After that, we used topology to generalize the basic rough set concepts and study their properties. It’s application in data reduction and decision analysis is investigated. Finally, a simple example is adopted to demonstrate the effectiveness of the proposed models.

<i>L</i>-fuzzy upper approximation operators associated with <i>L</i>-generalized fuzzy remote neighborhood systems of <i>L</i>-fuzzy points

It is well known that the approximation operators are always primitive concepts in kinds of general rough set theories. In this paper, considering L to be a completely distributive lattice, we introduce a notion of L-fuzzy upper approximation operator based on L-generalized fuzzy remote neighborhood systems of L-fuzzy points. It is shown that the new approximation operator is a fuzzification of the upper approximation operator in the rough set theory based on general remote neighborhood systems of classical points. Then the basic properties, axiomatic characterizations and the reduction theory on the L-fuzzy upper approximation operator are presented. Furthermore, the L-fuzzy upper approximation operators corresponding to the serial, reflexive, unary and transitive Lgeneralized fuzzy remote neighborhood systems, are discussed and characterized respectively.

Route classification scheme based on covering rough set approach in mobile ad hoc network (CRS-MANET)

PurposeThe purpose of this paper is to obtain correctly classified routes based on their parameters.Design/methodology/approachIn this paper, a covering rough set (CRS) approach is proposed for route classification in wireless ad hoc networks. In a wireless network, mobile nodes are deployed randomly in a simulation region. This work addresses the problem of route classification.FindingsThe network parameters such as bandwidth, delay, packet byte rate and packet loss rate changes due to the frequent mobility of nodes lead to uncertainty in wireless networks. This type of uncertainty can be very well handled using a rough set concept. An ultimate aim of classification is to correctly predict the decision class for each instance in the data.Originality/valueThe traditional classification algorithms, named K-nearest neighbor, J48, general rough set theory, naive Bayes, JRIP and multilayer perceptron, are used in this work for comparison and for the proposed CRS based on route classification approach revealing better accuracy than traditional classification algorithms.

Covering-based soft fuzzy rough theory and its application to multiple criteria decision making

Covering-based rough set model is a vital topic as a generalization of rough sets which is a tool for AI and data mining. For the purpose, we establish two classes of hybrid uncertain systems: soft rough fuzzy-covering models and soft fuzzy rough covering models by means of (fuzzy) soft neighborhoods. By means of fuzzy soft measure degrees, we deduce \(\alpha \)-soft rough fuzzy coverings, D-soft rough fuzzy coverings, \(\alpha \)-soft fuzzy rough coverings, and D-soft fuzzy rough coverings by these two hybrid uncertain systems, respectively. The relationships among the proposed covering-based rough set models are given. Based on the theoretical discussion for the combination of covering fuzzy rough sets and soft sets, we set forth a new method to multiple criteria decision-making problem. By comparative analysis, we obtain that the optimal results are the same between the aggregation operator method and our proposed method, which means that our method is reasonable and effective.

Generalizations of rough sets induced by binary relations approach in semigroups

Generalizations of rough sets induced by binary relations approach in semigroups

Covering-based general multigranulation intuitionistic fuzzy rough sets and corresponding applications to multi-attribute group decision-making

This paper concerns the intuitionistic fuzzy (IF) decision-making method for solving uncertain or vague problems. This traditional method has imperfections in some particular circumstances. For this reason, we combine rough set theory and the IF decision-making approach in order to design a novel procedure for making decisions. Several types of covering-based general multigranulation IF rough set (CGMIFRS) models are proposed by using four types of IF neighborhoods. A related example to illustrate these models is given. Furthermore, the relationships among the eight kinds of CGMIFRS models are also investigated. By the recourse to the principle of the PROMETHEE II method, a multi-attribute group decision-making (MAGDM) approach with IF information based on CGMIFRS models is set forth. A comparative analysis shows that the optimal objects of our method based on two IF logical operators, the IF PROMETHEE method and the IF aggregation operators are consistent. We conclude that our novel method is more effective to deal with MAGDM problems with IF information than the existing MAGDM methods.

On generalization of rough sets by using two different methods

On generalization of rough sets by using two different methods

On Characterization of Rough Type-2 Fuzzy Sets

Rough sets theory and fuzzy sets theory are important mathematical tools to deal with uncertainties. Rough fuzzy sets and fuzzy rough sets as generalizations of rough sets have been introduced. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle high uncertainties. In this paper, the rough type-2 fuzzy set model is proposed by combining the rough set theory with the type-2 fuzzy set theory. The rough type-2 fuzzy approximation operators induced from the Pawlak approximation space are defined. The rough approximations of a type-2 fuzzy set in the generalized Pawlak approximation space are also introduced. Some basic properties of the rough type-2 fuzzy approximation operators and the generalized rough type-2 fuzzy approximation operators are discussed. The connections between special crisp binary relations and generalized rough type-2 fuzzy approximation operators are further examined. The axiomatic characterization of generalized rough type-2 fuzzy approximation operators is also presented. Finally, the attribute reduction of type-2 fuzzy information systems is investigated.

Decision-theoretic rough sets under dynamic granulation

Decision-theoretic rough set theory is quickly becoming a research direction in rough set theory, which is a general and typical probabilistic rough set model with respect to its threshold semantics and decision features. However, unlike the Pawlak rough set, the positive region, the boundary region and the negative region of a decision-theoretic rough set are not monotonic as the number of attributes increases, which may lead to overlapping and inefficiency of attribute reduction with it. This may be caused by the introduction of a probabilistic threshold. To address this issue, based on the local rough set and the dynamic granulation principle proposed by Qian et al., this study will develop a new decision-theoretic rough set model satisfying the monotonicity of positive regions, in which the two parameters α and β need to dynamically update for each granulation. In addition to the semantic interpretation of its thresholds itself, the new model not only ensures the monotonicity of the positive region of a target concept (or decision), but also minimizes the local risk under each granulation. These advantages constitute important improvements of the decision-theoretic rough set model for its better and wider applications.

Distance based Attribute Reduction in Set-Valued Decision Tables

Rough set based attribute reduction is an important problem in pre-processing step in data mining. However, most rough set based attribute reduction methods perform on single-value decision tables. In this paper, we solve attribute reduction problems in set-valued decision tables. Our method uses the distance measure which constructed between a conditional attribute set and decision attribute. General Terms Rough set, decision table, set-valued decision table, attribute reduction.

General type-2 fuzzy rough sets based on $$\alpha $$ α -plane Representation theory

Rough sets theory and fuzzy sets theory are mathematical tools to deal with uncertainty, imprecision in data analysis. Traditional rough set theory is restricted to crisp environments. Since theories of fuzzy sets and rough sets are distinct and complementary on dealing with uncertainty, the concept of fuzzy rough sets has been proposed. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle highly uncertainties. Some researchers proposed interval type-2 fuzzy rough sets by combining interval type-2 fuzzy sets and rough sets. However, there are no reports about combining general type-2 fuzzy sets and rough sets. In addition, the $$\alpha $$ ? -plane representation method of general type-2 fuzzy sets has been extensively studied, and can reduce the computational workload. Motivated by the aforementioned accomplishments, in this paper, from the viewpoint of constructive approach, we first present definitions of upper and lower approximation operators of general type-2 fuzzy sets by using $$\alpha $$ ? -plane representation theory and study some basic properties of them. Furthermore, the connections between special general type-2 fuzzy relations and general type-2 fuzzy rough upper and lower approximation operators are also examined. Finally, in axiomatic approach, various classes of general type-2 fuzzy rough approximation operators are characterized by different sets of axioms.

Uncertainty measure for general relation-based rough fuzzy set

Purpose – The purpose of this paper is to present a measure method of the uncertainty for rough fuzzy set based on general binary relation. Design/methodology/approach – Rough set and fuzzy set are two different but complementary theories for expressing uncertainty information, and based on the combination of these two uncertainty theories of expressing and handling uncertainty information, the rough fuzzy set model and uncertainty measure based on general relation are discussed. Findings – This paper reveals the intrinsic of the uncertainty for rough fuzzy set based on general relation and presents a new measure method by introducing the Shannon entropy to generalized approximation space. Originality/value – The paper contributes to the discussion on the research of rough set and fuzzy set. The conclusions are useful in information processing with uncertainty.