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Rule acquisition and attribute reduction in real decision formal contexts

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Abstract

Formal Concept Analysis of real set formal contexts is a generalization of classical formal contexts. By dividing the attributes into condition attributes and decision attributes, the notion of real decision formal contexts is introduced. Based on an implication mapping, problems of rule acquisition and attribute reduction of real decision formal contexts are examined. The extraction of “if–then” rules from the real decision formal contexts, and the approach to attribute reduction of the real decision formal contexts are discussed. By the proposed approach, attributes which are non-essential to the maximal s rules or l rules (to be defined later in the text) can be removed. Furthermore, discernibility matrices and discernibility functions for computing the attribute reducts of the real decision formal contexts are constructed to determine all attribute reducts of the real set formal contexts without affecting the results of the acquired maximal s rules or l rules.

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Acknowledgments

The authors are grateful to the anonymous reviewers and the editor for their constructive comments and suggestions for the improvement of the paper. This work was supported by grants from the National Natural Science Foundation of China (No. 60963006), the Sino Social and Science Program of Ministry of Education (No: 09YJCZH082), and the Hong Kong Research Grants Council (CUHK 4126/04H).

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Authors and Affiliations

  1. Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, Shaan’xi, People’s Republic of China

    Hong-Zhi Yang

  2. Department of Geography and Resource Management, Center for Environmental Policy and Resource Management, University of Hong Kong, Hong Kong, People’s Republic of China

    Leung Yee

  3. Institute of Space and Earth Information Science, The Chinese University of Hong Kong, Hong Kong, People’s Republic of China

    Leung Yee

  4. College of Information Science and Technology, Shihezi University, Shihezi, 832000, Xinjiang, People’s Republic of China

    Ming-Wen Shao

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  1. Hong-Zhi Yang
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  2. Leung Yee
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  3. Ming-Wen Shao
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Correspondence to Ming-Wen Shao.

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Yang, HZ., Yee, L. & Shao, MW. Rule acquisition and attribute reduction in real decision formal contexts. Soft Comput 15, 1115–1128 (2011). https://doi.org/10.1007/s00500-010-0578-y

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