A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets

2007 ◽  
Vol 177 (17) ◽  
pp. 3500-3518 ◽  
Author(s):  
Chen Degang ◽  
Wang Changzhong ◽  
Hu Qinghua
Keyword(s):  
Rough Sets ◽  
Attribute Reduction ◽  
New Approach ◽  
Decision Systems

scholarly journals A Neighborhood Rough Sets-Based Attribute Reduction Method Using Lebesgue and Entropy Measures

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 138 ◽  
Author(s):  
Lin Sun ◽  
Lanying Wang ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Rough Sets ◽  
Reduction Method ◽  
Attribute Reduction ◽  
Numerical Data ◽  
Classification Performance ◽  
Data Sets ◽  
Decision Systems ◽  
Public Data ◽  
Entropy Measures ◽  
Neighborhood Rough Sets

For continuous numerical data sets, neighborhood rough sets-based attribute reduction is an important step for improving classification performance. However, most of the traditional reduction algorithms can only handle finite sets, and yield low accuracy and high cardinality. In this paper, a novel attribute reduction method using Lebesgue and entropy measures in neighborhood rough sets is proposed, which has the ability of dealing with continuous numerical data whilst maintaining the original classification information. First, Fisher score method is employed to eliminate irrelevant attributes to significantly reduce computation complexity for high-dimensional data sets. Then, Lebesgue measure is introduced into neighborhood rough sets to investigate uncertainty measure. In order to analyze the uncertainty and noisy of neighborhood decision systems well, based on Lebesgue and entropy measures, some neighborhood entropy-based uncertainty measures are presented, and by combining algebra view with information view in neighborhood rough sets, a neighborhood roughness joint entropy is developed in neighborhood decision systems. Moreover, some of their properties are derived and the relationships are established, which help to understand the essence of knowledge and the uncertainty of neighborhood decision systems. Finally, a heuristic attribute reduction algorithm is designed to improve the classification performance of large-scale complex data. The experimental results under an instance and several public data sets show that the proposed method is very effective for selecting the most relevant attributes with high classification accuracy.

A new approach of attribute reduction of rough sets based on soft metric

2020 ◽  
Vol 39 (3) ◽  
pp. 4473-4489
Author(s):  
H.I. Mustafa ◽  
O.A. Tantawy
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Attribute Reduction ◽  
Feature Subset Selection ◽  
Feature Subset ◽  
Data Set ◽  
Decision Systems ◽  
Proposed Model ◽  
Processing Step ◽  
Important Processing

Attribute reduction is considered as an important processing step for pattern recognition, machine learning and data mining. In this paper, we combine soft set and rough set to use them in applications. We generalize rough set model and introduce a soft metric rough set model to deal with the problem of heterogeneous numerical feature subset selection. We construct a soft metric on the family of knowledge structures based on the soft distance between attributes. The proposed model will degrade to the classical one if we specify a zero soft real number. We also provide a systematic study of attribute reduction of rough sets based on soft metric. Based on the constructed metric, we define co-information systems and consistent co-decision systems, and we provide a new method of attribute reductions of each system. Furthermore, we present a judgement theorem and discernibility matrix associated with attribute of each type of system. As an application, we present a case study from Zoo data set to verify our theoretical results.

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.

scholarly journals Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Aiping Huang ◽  
William Zhu
Keyword(s):  
Rough Sets ◽  
Optimization Problems ◽  
Lattice Structure ◽  
Attribute Reduction ◽  
Algorithm Design ◽  
Geometric Lattice ◽  
Closed Sets ◽  
Decision Systems ◽  
Dependence Space ◽  
Geometric Lattices

The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice, to study the attribute reduction issues of information systems.

scholarly journals Approximate Accuracy Approaches to Attribute Reduction for Information Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Deshan Liu ◽  
Dapeng Wang ◽  
Deqin Yan ◽  
Yu Sang
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Rough Sets ◽  
Attribute Reduction ◽  
New Approach ◽  
Rough Sets Theory ◽  
Incomplete Information Systems ◽  
Sets Theory ◽  
Novel Algorithm

The key problem for attribute reduction to information systems is how to evaluate the importance of an attribute. The algorithms are challenged by the variety of data forms in information system. Based on rough sets theory we present a new approach to attribute reduction for incomplete information systems and fuzzy valued information systems. In order to evaluate the importance of an attribute effectively, a novel algorithm with rigorous theorem is proposed. Experiments show the effect of proposed algorithm.

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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