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Continuous lattices in formal concept analysis

  • Fuzzy systems and their mathematics
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Abstract

We introduce the notions of augmented formal contexts and generalized approximable concepts and show that all the generalized approximable concepts of an augmented formal context generates a continuous lattice under inclusion order, on the contrary, each continuous lattice can be obtained by this way. Furthermore, the notion of C-mappings is proposed between augmented formal contexts to obtain a category of augmented formal contexts. Then we show the category is equivalent to that of continuous lattices whose morphisms are Scott continuous functions.

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Funding

This work was supported by the National Natural Science Foundation of China (12231007) and the Young Scholars Science Foundation of Lanzhou Jiaotong University (2022025).

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Authors and Affiliations

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, 730070, Gansu, China

    Lingjuan Yao

  2. School of Mathematics and Statistics, Liupanshui Normal University, Minghu Road, LiuPanshui, 553004, Guizhou, China

    Shengwen Wang

  3. School of Mathematics, Hunan University, Changsha, 410082, Hunan, China

    Qingguo Li & Mingjie Cai

Authors
  1. Lingjuan Yao
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  2. Shengwen Wang
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  3. Qingguo Li
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  4. Mingjie Cai
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All authors contributed equally to the writing of this paper..

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Correspondence to Shengwen Wang.

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Yao, L., Wang, S., Li, Q. et al. Continuous lattices in formal concept analysis. Soft Comput 28, 955–962 (2024). https://doi.org/10.1007/s00500-023-09462-5

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