A novel and better fitness evaluation for rough set based minimum attribute reduction problem

2013 ◽  
Vol 222 ◽  
pp. 413-423 ◽  
Author(s):  
Dongyi Ye ◽  
Zhaojiong Chen ◽  
Shenglan Ma
Keyword(s):  
Rough Set ◽  
Attribute Reduction ◽  
Fitness Evaluation ◽  
Reduction Problem

scholarly journals Test-Cost-Sensitive Attribute Reduction of Data with Normal Distribution Measurement Errors

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hong Zhao ◽  
Fan Min ◽  
William Zhu
Keyword(s):  
Measurement Error ◽  
Normal Distribution ◽  
Uniform Distribution ◽  
Rough Set ◽  
Measurement Errors ◽  
Attribute Reduction ◽  
Distribution Measurement ◽  
Test Cost ◽  
Reduction Problem ◽  
Sensitive Attribute

The measurement error with normal distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making, we will select an attribute subset with appropriate measurement error to minimize the total test cost. Recently, error-range-based covering rough set with uniform distribution error was proposed to investigate this issue. However, the measurement errors satisfy normal distribution instead of uniform distribution which is rather simple for most applications. In this paper, we introduce normal distribution measurement errors to covering-based rough set model and deal with test-cost-sensitive attribute reduction problem in this new model. The major contributions of this paper are fourfold. First, we build a new data model based on normal distribution measurement errors. Second, the covering-based rough set model with measurement errors is constructed through the “3-sigma” rule of normal distribution. With this model, coverings are constructed from data rather than assigned by users. Third, the test-cost-sensitive attribute reduction problem is redefined on this covering-based rough set. Fourth, a heuristic algorithm is proposed to deal with this problem. The experimental results show that the algorithm is more effective and efficient than the existing one. This study suggests new research trends concerning cost-sensitive learning.

scholarly journals Cost-Sensitive Attribute Reduction in Decision-Theoretic Rough Set Models

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shujiao Liao ◽  
Qingxin Zhu ◽  
Fan Min
Keyword(s):  
Rough Set ◽  
Optimization Problem ◽  
Heuristic Algorithms ◽  
Attribute Reduction ◽  
Test Cost ◽  
Reduction Problem ◽  
Sensitive Attribute ◽  
Definition Of ◽  
Insight Into ◽  
Decision Cost

In recent years, the theory of decision-theoretic rough set and its applications have been studied, including the attribute reduction problem. However, most researchers only focus on decision cost instead of test cost. In this paper, we study the attribute reduction problem with both types of costs in decision-theoretic rough set models. A new definition of attribute reduct is given, and the attribute reduction is formulated as an optimization problem, which aims to minimize the total cost of classification. Then both backtracking and heuristic algorithms to the new problem are proposed. The algorithms are tested on four UCI (University of California, Irvine) datasets. Experimental results manifest the efficiency and the effectiveness of both algorithms. This study provides a new insight into the attribute reduction problem in decision-theoretic rough set models.

scholarly journals The Relationship between the Unicost Set Covering Problem and the Attribute Reduction Problem in Rough Set Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Qingyuan Xu ◽  
Jinjin Li
Keyword(s):  
Rough Set ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Set Covering ◽  
Covering Problem ◽  
Set Covering Problem ◽  
Reduction Problem ◽  
Covering Model ◽  
The Relationship ◽  
Unicost Set Covering Problem

The unicost set covering problem and the attribute reduction problem are NP-complete problems. In this paper, the relationship between these two problems are discussed. Based on the transformability between attribute reductions and minimal solutions in unicost set covering models, two methods are provided. One is to induce an information table from a given unicost set covering model. With no doubt, it shows that the unicost set covering problem can be investigated by rough set theory. The other is to induce a unicost set covering model from a given information table. Similarly, it shows that the attribute reduction problem can be studied by set covering theory. As an application of the proposed theoretical results, a rough set heuristic algorithm is presented for the unicost set covering problem.

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.

Research on RS-WNN Integrated Modeling

2011 ◽  
Vol 105-107 ◽  
pp. 2169-2173
Author(s):  
Zong Chang Xu ◽  
Xue Qin Tang ◽  
Shu Feng Huang
Keyword(s):  
Neural Network ◽  
Rough Set ◽  
Attribute Reduction ◽  
Wavelet Neural Network ◽  
Integrated Modeling ◽  
Generalization Ability ◽  
Decision Attributes ◽  
Optimum Decision ◽  
Structure Complexity ◽  
Modeling Algorithm

Wavelet Neural Network (WNN) integration modeling based on Rough Set (RS) is studied. An integration modeling algorithm named RS-WNN, which first introduces a heuristic attribute reduction recursion algorithm to determine the optimum decision attributes and then conducts WNN modeling, is proposed. This method is adopted to more effectively eliminate the redundant attributes, lower the structure complexity of WNN, which reduce the time of training and improve the generalization ability of WNN. The result of the experiment shows this method is superior and efficient.

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.

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