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Decomposition methods of formal contexts to construct concept lattices

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Abstract

As an important tool for data analysis and knowledge processing, formal concept analysis has been applied to many fields. In this paper, we introduce a decomposition method of a formal context to construct its corresponding concept lattice, which answers an open problem to some extent that how this decomposition method of a context translates into a decomposition method of its corresponding concept lattice. Firstly, based on subcontext, closed relation and pairwise noninclusion covering on the attribute set, we obtain the decomposition theory of a formal context, and then we provide the method and algorithm of constructing the corresponding concept lattice by using this decomposition theory. Moreover, we consider the similar decomposition theory and method of a formal context from the object set. Finally, we make another decomposition of a formal context by combining the above two results.

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Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 11371014 and 11071281), the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2014JM8306) and the State Scholarship Fund of China.

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Authors and Affiliations

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

    Ting Qian & Ling Wei

  2. College of Science, Xi’an Shiyou University, Xi’an, 710065, China

    Ting Qian

  3. School of Computer Science and Technology, Xidian University, Xi’an, 710071, China

    Jianjun Qi

Authors
  1. Ting Qian
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  2. Ling Wei
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  3. Jianjun Qi
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Correspondence to Ling Wei.

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Qian, T., Wei, L. & Qi, J. Decomposition methods of formal contexts to construct concept lattices. Int. J. Mach. Learn. & Cyber. 8, 95–108 (2017). https://doi.org/10.1007/s13042-016-0578-z

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  • DOI: https://doi.org/10.1007/s13042-016-0578-z

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