Maximal and stochastic Galois lattices

被引：23

作者：

Diday, E ^{[1
]}

Emilion, R

机构：

[1] Univ Paris 09, CEREMADE, F-75016 Paris, France

[2] Univ Paris 10, SEGMI Modalx, F-92000 Nanterre, France

来源：

DISCRETE APPLIED MATHEMATICS | 2003年 / 127卷 / 02期

关键词：

association rules; capacity; data mining; extent; formal concepts; fuzzy Galois lattices; Galois lattices; intent; stochastic Galois lattices; stochastic order; t-conorm; t-norm;

D O I：

10.1016/S0166-218X(02)00210-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2003 Elsevier Science B.V. All rights reserved.

引用

页码：271 / 284

页数：14