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Concept lattice on cubic sets. (English) Zbl 1474.06021

Summary: In 2012, Y. B. Jun et al. [Ann. Fuzzy Math. Inform. 4, No. 1, 83–98 (2012; Zbl 1301.03048)] introduced the notion of a cubic set, which is a generalization of Zadeh’s fuzzy set. In 1999, B. Ganter and R. Wille [Formal concept analysis. Mathematical foundations. Transl. from the German by Cornelia Franzke. Berlin: Springer (1999; Zbl 0909.06001)] put forward formal concept analysis theory (FCA), formal context, concept lattice are two main notions and tools. In the paper, we define formal context, Galois connection, concept lattice on cubic sets, and generalize formal concept analysis theory on cubic sets structure.

MSC:

06B23 Complete lattices, completions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
68T30 Knowledge representation
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