Maximal and Stochastic Galois Lattices

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 de0ned 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 de0ned by distributions are limit of empirical Galois lattices nodes. Choquet capacities, t-norms and t-conorms appear as natural valuations of these lattices. ? 2003 Elsevier Science B.V. All rights reserved.