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On multi-adjoint concept lattices: definition and representation theorem. (English) Zbl 1187.68588

Kuznetsov, Sergei O. (ed.) et al., Formal concept analysis. 5th international conference, ICFCA 2007, Clermont-Ferrand, France, February 12–16, 2007. Proceedings. (ISBN 978-3-540-70828-5/pbk). Lecture Notes in Computer Science 4390. Lecture Notes in Artificial Intelligence, 197-209 (2007).
Summary: Several fuzzifications of formal concept analysis have been proposed to deal with uncertainty or incomplete information. In this paper, we focus on the new paradigm of multi-adjoint concept lattices which embeds different fuzzy extensions of concept lattices, our main result being the representation theorem of this paradigm. As a consequence of this theorem, the representation theorems of the other paradigms can be proved more directly. Moreover, the multi-adjoint paradigm enriches the language providing greater flexibility to the user.
For the entire collection see [Zbl 1115.68004].

MSC:

68T30 Knowledge representation
06A15 Galois correspondences, closure operators (in relation to ordered sets)
06B99 Lattices
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