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 Attribute Reduction Based on Consistent Covering Rough Set and Its Application

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jianchuan Bai ◽  
Kewen Xia ◽  
Yongliang Lin ◽  
Panpan Wu
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Relevance Vector Machine ◽  
Support Vector ◽  
Processing Step ◽  
Important Processing ◽  
Continuous Attribute ◽  
Covering Rough Set

As an important processing step for rough set theory, attribute reduction aims at eliminating data redundancy and drawing useful information. Covering rough set, as a generalization of classical rough set theory, has attracted wide attention on both theory and application. By using the covering rough set, the process of continuous attribute discretization can be avoided. Firstly, this paper focuses on consistent covering rough set and reviews some basic concepts in consistent covering rough set theory. Then, we establish the model of attribute reduction and elaborate the steps of attribute reduction based on consistent covering rough set. Finally, we apply the studied method to actual lagging data. It can be proved that our method is feasible and the reduction results are recognized by Least Squares Support Vector Machine (LS-SVM) and Relevance Vector Machine (RVM). Furthermore, the recognition results are consistent with the actual test results of a gas well, which verifies the effectiveness and efficiency of the presented method.

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.

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.

Attribute reduction in fuzzy multi-covering decision systems via observational- consistency and fuzzy discernibility

2021 ◽  
pp. 1-15
Author(s):  
Rongde Lin ◽  
Jinjin Li ◽  
Dongxiao Chen ◽  
Jianxin Huang ◽  
Yingsheng Chen
Keyword(s):  
Rough Set ◽  
Attribute Reduction ◽  
Recursive Method ◽  
Redundant Information ◽  
Reduction Algorithm ◽  
Discernibility Matrix ◽  
Decision Systems ◽  
Theoretical Tool ◽  
Lower Ratio ◽  
Covering Rough Set

Fuzzy covering rough set model is a popular and important theoretical tool for computation of uncertainty, and provides an effective approach for attribute reduction. However, attribute reductions derived directly from fuzzy lower or upper approximations actually still occupy large of redundant information, which leads to a lower ratio of attribute-reduced. This paper introduces a kind of parametric observation sets on the approximations, and further proposes so called parametric observational-consistency, which is applied to attribute reduction in fuzzy multi-covering decision systems. Then the related discernibility matrix is developed to provide a way of attribute reduction. In addition, for multiple observational parameters, this article also introduces a recursive method to gradually construct the multiple discernibility matrix by composing the refined discernibility matrix and incremental discernibility matrix based on previous ones. In such case, an attribute reduction algorithm is proposed. Finally, experiments are used to demonstrate the feasibility and effectiveness of our proposed method.

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.

Intuitionistic Fuzzy Neighborhood Rough Set Model for Feature Selection

2018 ◽  
Vol 7 (2) ◽  
pp. 75-84 ◽  
Author(s):  
Shivam Shreevastava ◽  
Anoop Kumar Tiwari ◽  
Tanmoy Som
Keyword(s):  
Feature Selection ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Continuous Data ◽  
Feature Subset ◽  
Data Set ◽  
Intuitionistic Fuzzy ◽  
Neighborhood Models ◽  
Neighborhood Rough Set

Feature selection is one of the widely used pre-processing techniques to deal with large data sets. In this context, rough set theory has been successfully implemented for feature selection of discrete data set but in case of continuous data set it requires discretization, which may cause information loss. Fuzzy rough set theory approaches have also been used successfully to resolve this issue as it can handle continuous data directly. Moreover, almost all feature selection techniques are used to handle homogeneous data set. In this article, the center of attraction is on heterogeneous feature subset reduction. A novel intuitionistic fuzzy neighborhood models have been proposed by combining intuitionistic fuzzy sets and neighborhood rough set models by taking an appropriate pair of lower and upper approximations and generalize it for feature selection, supported with theory and its validation. An appropriate algorithm along with application to a data set has been added.

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