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Dependence-space-based attribute reduction in consistent decision tables

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Abstract

This paper proposes a novel approach to attribute reduction in consistent decision tables within the framework of dependence spaces. For a consistent decision table \((U,A\cup \{d\}),\) an equivalence relation r on the conditional attribute set A and a congruence relation R on the power set of A are constructed, respectively. Two closure operators, T r and T R , and two families of closed sets, \({\mathcal C}_r\) and \({\mathcal C}_R,\) are then constructed with respect to the two equivalence relations. After discussing the properties of \({\mathcal C}_r\) and \({\mathcal C}_R,\) the necessary and sufficient condition for \({\mathcal C}_r={\mathcal C}_R\) is obtained and employed to formulate an approach to attribute reduction in consistent decision tables. It is also proved, under the condition \({\mathcal C}_r={\mathcal C}_R,\) that a relative reduct is equivalent to a \(R\)-reduction defined by Novotny and Pawlak (Fundam Inform 16:275–287, 1992).

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Acknowledgments

This work was supported by the earmarked grant CUHK 4126/04H of the Hong Kong Research Grants Council.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, Hebei, People’s Republic of China

    Ju-Sheng Mi

  2. Department of Geography and Resource Management, Center for Environmental Policy and Resource Management, and Institute of Space and Earth Information Science, The Chinese University of Hong Kong, Hong Kong, People’s Republic of China

    Yee Leung

  3. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316004, Zhejiang, People’s Republic of China

    Wei-Zhi Wu

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  1. Ju-Sheng Mi
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Correspondence to Ju-Sheng Mi.

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Mi, JS., Leung, Y. & Wu, WZ. Dependence-space-based attribute reduction in consistent decision tables. Soft Comput 15, 261–268 (2011). https://doi.org/10.1007/s00500-010-0656-1

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