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A generalized concept lattice. (English) Zbl 1088.06005
Summary: We describe a new approach to fuzzify a concept lattice and we show that it is a generalization and common platform for already known approaches: the classical crisp Ganter & Wille [B. Ganter and R. Wille, Formal concept analysis. Berlin: Springer (1999; Zbl 0909.06001)] case, the fuzzy Pollandt [S. Pollandt, in: G. Stumme et al. (eds.), Begriffliche Wissensverarbeitung. Methoden und Anwendungen. Berlin: Springer, 72–98 (2000; Zbl 0958.68162)] and Bělohlávek [R. Bělohlávek, Ann. Pure Appl. Logic 128, 277–298 (2004; Zbl 1060.03040)] ones, and the one-sided fuzzy concept lattice [S. Ben Yahia and A. Jaoua, “Discovering knowledge from fuzzy concept lattice”, in: A. Kandel et al. (eds.), Data mining and computational intelligence. Stud. Fuzziness Soft Comput. 68. Heidelberg: Physica-Verlag, 169–190 (2001; Zbl 1022.68034)]. We define appropriate (symmetric) mappings and show that they form a Galois connection. In the end we show that these mappings generate a complete lattice.

MSC:
06B23 Complete lattices, completions
06D72 Fuzzy lattices (soft algebras) and related topics
68T30 Knowledge representation
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