Maximal and stochastic Galois lattices

Authors:
Edwin Diday;Richard Emilion
Affiliations:
CEREMADE, Université Paris-Dauphine, 75106 Paris, France;SEGMI-Modalx, Université Paris X, 92000 Nanterre, France
Venue:
Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
Year:
2003

Citing 1
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Abstract

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.