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Attribute reduction theory of concept lattice based on decision formal contexts

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Abstract

The theory of concept lattices is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. Based on the reduction theory of classical formal context, this paper proposes the definition of decision formal context and its reduction theory, which extends the reduction theory of concept lattices. In this paper, strong consistence and weak consistence of decision formal context are defined respectively. For strongly consistent decision formal context, the judgment theorems of consistent sets are examined, and approaches to reduction are given. For weakly consistent decision formal context, implication mapping is defined, and its reduction is studied. Finally, the relation between reducts of weakly consistent decision formal context and reducts of implication mapping is discussed.

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Authors and Affiliations

  1. Department of Mathematics, Northwest University, Xi’an, 710069, China

    Ling Wei

  2. School of Computer Science & Technology, Xidian University, Xi’an, 710071, China

    JianJun Qi

  3. Institute for Information and System Sciences, Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, China

    WenXiu Zhang

Authors
  1. Ling Wei
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  2. JianJun Qi
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  3. WenXiu Zhang
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Corresponding author

Correspondence to Ling Wei.

Additional information

Supported by the National 973 Program of China (Grant No. 2002CB312200), the National Natural Science Foundation of China (Grant Nos. 60703117, 60433010 and 60673096), and the Doctor Research Fund of Northwest University in China

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Wei, L., Qi, J. & Zhang, W. Attribute reduction theory of concept lattice based on decision formal contexts. Sci. China Ser. F-Inf. Sci. 51, 910–923 (2008). https://doi.org/10.1007/s11432-008-0067-4

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  • DOI: https://doi.org/10.1007/s11432-008-0067-4

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