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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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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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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DOI: https://doi.org/10.1007/s00500-023-09462-5