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Maximal and stochastic Galois Lattices

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Date
2003-06
Dewey
Probabilités et mathématiques appliquées
Sujet
Treillis de Galois stochastiques
Journal issue
Discrete Applied Mathematics
Volume
2
Number
127
Publication date
12-2003
Article pages
271-284
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/S0166-218X(02)00210-X
URI
https://basepub.dauphine.fr/handle/123456789/1954
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  • CEREMADE : Publications
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Author
Diday, Edwin
Emilion, Richard
Type
Article accepté pour publication ou publié
Abstract (EN)
We present a general formula for the intent–extent mappings of a Galois lattice generated by individual descriptions which lie in any arbitrary lattice. The formulation is unique if a natural maximality condition is required. This formulation yields, as particular cases, formal concept binary Galois lattices of Wille, those defined by Brito or Blyth–Janowitz, as well as fuzzy or stochastic Galois lattices. For the case of random descriptors we show that the nodes of Galois lattices defined by distributions are limit of empirical Galois lattices nodes. Choquet capacities, t-norms and t-conorms appear as natural valuations of these lattices. Author Keywords: Association rules; Capacity; Data mining; Extent; Formal concepts; Fuzzy Galois lattices; Galois lattices; Intent; Stochastic Galois lattices; Stochastic order; t-conorm; t-norm

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