Roughness measure based on description ability for attribute reduction in information system
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ORIGINAL ARTICLE
Roughness measure based on description ability for attribute reduction in information system Fachao Li1 · Chenxia Jin1 · Jinning Yang2 Received: 10 May 2016 / Accepted: 18 December 2017 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract As a quantitative index of processing uncertain information by rough set theory, roughness measure is the basis of many decision-making problems such as resource management, system optimization etc. Therefore constructing roughness measure reflecting different decision preference has important theoretical and practical value. In this paper, we first analyze the characteristics and deficiencies of Pawlak roughness, and further propose the concepts of lower (upper) accuracy. We second establish an description ability-based roughness measure (DRD) by combining with two basic measure factors-lower (upper) accuracy. We third analyze the characteristics of DRD and further give some sufficient and necessary conditions. Finally, we propose a DRD-based reduction method (DRD-RM), and discuss the difference and relation between DRD-RM and the existing reduction methods by experimental analysis for UCI data. The experimental results show that DRD-RM is an effective technique. Keywords Roughness · Lower (upper) accuracy · Description ability · Attribute Reduction
1 Introduction Rough set theory proposed by Pawlak [1] has been used as a powerful data processing tool to discover data dependencies and knowledge hidden in a decision information system. It can provide a formal methodology to deal with various types of imprecise and uncertain data analysis problems. Attribute reduction is one of the most fundamental and important concept in rough set theory. It plays an essential role in numerous areas including pattern recognition, data mining, machine learning and decision analysis [2–6]. It has been drawing wide attention in recent years, which can be mainly classified into two categories [7]: one concentrates on algebra methods-based reduction, the other focus on information * Chenxia Jin [email protected] Fachao Li [email protected] Jinning Yang [email protected] 1
School of Economics and Management, Hebei University of Science and Technology, Shijiazhuang 050018, China
EBUPT Information Technology Co., Ltd., Beijing 100000, China
2
entropy methods-based reduction. The algebra methods reduction mainly define a reduct by some criteria, such as qualities of classification, maximum distribution preservation etc. For example, Pawlak [1] proposed an attribute reduction method that does not change the positive region or the quality of classification; Skowron [8] introduced the concepts of the discernibility matrix and discernibility function for reduct in information systems. Radaideh [9] proposed an approximate reduct approach which used the discernibility matrix concept and a weighting mechanism to determine the significance of an attribute. Wroblewski [10] introduced the notion of approximate reduct and discussed some proposals of quality
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