ON ATTRIBUTE REDUCTION WITH INTUITIONISTIC FUZZY ROUGH SETS

2012 ◽  
Vol 20 (01) ◽  
pp. 59-76 ◽  
Author(s):  
ZHIMING ZHANG ◽  
JINGFENG TIAN
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Theoretical Foundation ◽  
Attribute Reduction ◽  
Upper Approximation ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Rough Sets ◽  
Axiomatic Approaches

Intuitionistic fuzzy (IF) rough sets are the generalization of traditional rough sets obtained by combining the IF set theory and the rough set theory. The existing research on IF rough sets mainly concentrates on the establishment of lower and upper approximation operators using constructive and axiomatic approaches. Less effort has been put on the attribute reduction of databases based on IF rough sets. This paper systematically studies attribute reduction based on IF rough sets. Firstly, attribute reduction with traditional rough sets and some concepts of IF rough sets are reviewed. Then, we introduce some concepts and theorems of attribute reduction with IF rough sets, and completely investigate the structure of attribute reduction. Employing the discernibility matrix approach, an algorithm to find all attribute reductions is also presented. Finally, an example is proposed to illustrate our idea and method. Altogether, these findings lay a solid theoretical foundation for attribute reduction based on IF rough sets.

scholarly journals Covering-Based Rough Sets on Eulerian Matroids

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bin Yang ◽  
Ziqiong Lin ◽  
William Zhu
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Closure Operator ◽  
Matroid Theory ◽  
Upper Approximation ◽  
Significant Generalization ◽  
Eulerian Matroid ◽  
Vital Structure

Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids.

Model of Covering Rough Sets in the Machine Intelligence

2012 ◽  
Vol 548 ◽  
pp. 735-739
Author(s):  
Hong Mei Nie ◽  
Jia Qing Zhou
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Machine Intelligence ◽  
Upper Approximation ◽  
Generalized Rough Sets

Rough set theory has been proposed by Pawlak as a useful tool for dealing with the vagueness and granularity in information systems. Classical rough set theory is based on equivalence relation. The covering rough sets are an improvement of Pawlak rough set to deal with complex practical problems which the latter one can not handle. This paper studies covering-based generalized rough sets. In this setting, we investigate common properties of classical lower and upper approximation operations hold for the covering-based lower and upper approximation operations and relationships among some type of covering rough sets.

scholarly journals Parallel Attribute Reduction Algorithm for Complex Heterogeneous Data Using MapReduce

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Tengfei Zhang ◽  
Fumin Ma ◽  
Jie Cao ◽  
Chen Peng ◽  
Dong Yue
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Heterogeneous Data ◽  
Reduction Algorithm ◽  
Numerical Attributes ◽  
Reduction Efficiency ◽  
Speed Up

Parallel attribute reduction is one of the most important topics in current research on rough set theory. Although some parallel algorithms were well documented, most of them are still faced with some challenges for effectively dealing with the complex heterogeneous data including categorical and numerical attributes. Aiming at this problem, a novel attribute reduction algorithm based on neighborhood multigranulation rough sets was developed to process the massive heterogeneous data in the parallel way. The MapReduce-based parallelization method for attribute reduction was proposed in the framework of neighborhood multigranulation rough sets. To improve the reduction efficiency, the hashing Map/Reduce functions were designed to speed up the positive region calculation. Thereafter, a quick parallel attribute reduction algorithm using MapReduce was developed. The effectiveness and superiority of this parallel algorithm were demonstrated by theoretical analysis and comparison experiments.

scholarly journals Multigranulations Rough Set Method of Attribute Reduction in Information Systems Based on Evidence Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Minlun Yan
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Decision Rules ◽  
Evidence Theory ◽  
Point Of View ◽  
Upper Approximation

Attribute reduction is one of the most important problems in rough set theory. However, from the granular computing point of view, the classical rough set theory is based on a single granulation. It is necessary to study the issue of attribute reduction based on multigranulations rough set. To acquire brief decision rules from information systems, this paper firstly investigates attribute reductions by combining the multigranulations rough set together with evidence theory. Concepts of belief and plausibility consistent set are proposed, and some important properties are addressed by the view of the optimistic and pessimistic multigranulations rough set. What is more, the multigranulations method of the belief and plausibility reductions is constructed in the paper. It is proved that a set is an optimistic (pessimistic) belief reduction if and only if it is an optimistic (pessimistic) lower approximation reduction, and a set is an optimistic (pessimistic) plausibility reduction if and only if it is an optimistic (pessimistic) upper approximation reduction.

scholarly journals An Attribute Reduction Method using Neighborhood Entropy Measures in Neighborhood Rough Sets

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 155 ◽  
Author(s):  
Lin Sun ◽  
Xiaoyu Zhang ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Classification Performance ◽  
Data Sets ◽  
Complex Data ◽  
Decision Systems ◽  
Neighborhood Rough Sets

Attribute reduction as an important preprocessing step for data mining, and has become a hot research topic in rough set theory. Neighborhood rough set theory can overcome the shortcoming that classical rough set theory may lose some useful information in the process of discretization for continuous-valued data sets. In this paper, to improve the classification performance of complex data, a novel attribute reduction method using neighborhood entropy measures, combining algebra view with information view, in neighborhood rough sets is proposed, which has the ability of dealing with continuous data whilst maintaining the classification information of original attributes. First, to efficiently analyze the uncertainty of knowledge in neighborhood rough sets, by combining neighborhood approximate precision with neighborhood entropy, a new average neighborhood entropy, based on the strong complementarity between the algebra definition of attribute significance and the definition of information view, is presented. Then, a concept of decision neighborhood entropy is investigated for handling the uncertainty and noisiness of neighborhood decision systems, which integrates the credibility degree with the coverage degree of neighborhood decision systems to fully reflect the decision ability of attributes. Moreover, some of their properties are derived and the relationships among these measures are established, which helps to understand the essence of knowledge content and the uncertainty of neighborhood decision systems. Finally, a heuristic attribute reduction algorithm is proposed to improve the classification performance of complex data sets. The experimental results under an instance and several public data sets demonstrate that the proposed method is very effective for selecting the most relevant attributes with great classification performance.

Generalized dynamic attribute reduction based on similarity relation of intuitionistic fuzzy rough set

2020 ◽  
Vol 39 (5) ◽  
pp. 7107-7122
Author(s):  
Zhang Chuanchao
Keyword(s):  
Big Data ◽  
Information Systems ◽  
Rough Set ◽  
Rough Sets ◽  
Attribute Reduction ◽  
Similarity Relation ◽  
Fuzzy Rough Set ◽  
Data Set ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Rough Sets

In view of the characteristics with big data, high feature dimension, and dynamic for a large-scale intuitionistic fuzzy information systems, this paper integrates intuitionistic fuzzy rough sets and generalized dynamic sampling theory, proposes a generalized attribute reduction algorithm based on similarity relation of intuitionistic fuzzy rough sets and dynamic reduction. It uses dynamic reduction sampling theory to divide a big data set into small data sets and relative positive domain cardinality instead of dependency degree as decision-making condition, and obtains reduction attributes of big intuitionistic fuzzy decision information systems, and achieves the goal of extracting key features and fault diagnosis. The innovation of this paper is that it integrates generalized dynamic reduction and intuitionistic fuzzy rough set, and solves the problem of big data set which cannot be solved by intuitionistic fuzzy rough set. Taking an actual data as an example, the scientificity, rationality and effectiveness of the algorithm are verified from the aspects of stability, diagnostic accuracy, optimization ability and time complexity. Compared with similar algorithms, the advantages of the proposed algorithm for big data processing are confirmed.

Entropy Based Attribute Reduction Algorithms for Rough Sets

2012 ◽  
Vol 268-270 ◽  
pp. 1859-1862
Author(s):  
Hua Yan
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Calculation Result ◽  
Rough Sets ◽  
Traditional Method ◽  
Rough Set Theory ◽  
Attribute Reduction

This paper presented a concept of knowledge entropy, and according to this concept the importance of attribute was defined. Algorithms for attribute reduction in rough sets based on concept of knowledge entropy was given, and an example analysis was done in this paper. For the example, the calculation result is coincident with the result calculated by using the traditional method of attribute reduction in rough set theory.

Analysing diabetes using rough sets

2020 ◽  
pp. 533-538
Author(s):  
S. Arjun Raj ◽  
M. Vigneshwaran
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
International Diabetes Federation ◽  
Published Data ◽  
Lower And Upper Approximations

In this article we use the rough set theory to generate the set of decision concepts in order to solve a medical problem.Based on officially published data by International Diabetes Federation (IDF), rough sets have been used to diagnose Diabetes.The lower and upper approximations of decision concepts and their boundary regions have been formulated here.

scholarly journals Parametric Matroid of Rough Set

2015 ◽  
Vol 23 (06) ◽  
pp. 893-908 ◽  
Author(s):  
Yanfang Liu ◽  
Hong Zhao ◽  
William Zhu
Keyword(s):  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Independent Set ◽  
Approximation Operator ◽  
Approximation Number ◽  
Lower Approximation ◽  
The One

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a generalization of linear algebra and graph theory. Recently, a matroidal structure of rough sets is established and applied to the problem of attribute reduction which is an important application of rough set theory. In this paper, we propose a new matroidal structure of rough sets and call it a parametric matroid. On the one hand, for an equivalence relation on a universe, a parametric set family, with any subset of the universe as its parameter, is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore a matroid is generated, and we call it a parametric matroid of the rough set. Through the lower approximation operator, three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, partition-circuit matroids are well studied through the lower approximation number, and then we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.

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