Lattice-theoretic contexts and their concept lattices via Galois ideals
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- 作者：Wei Yao<sup> ; sup><sup>asup><sup> ; sup><sup>yaowei0516@163.com" class="auth_mail" title="E-mail the corresponding authorsup><sup> ; sup><sup>yaowei0516@126.com" class="auth_mail" title="E-mail the corresponding authorsup> ; Sang-Eon Han<sup>bsup> ; Rongxin Wang<sup>asup>
- 关键词：Power context ; Galois connection ; Galois ideal ; Lattice-theoretic context ; Concept lattice ; Formal fuzzy context
- 刊名：Information Sciences
- 出版年：2016
- 出版时间：20 April 2016
- 年：2016
- 卷：339
- 期：Complete
- 页码：1-18
- 全文大小：601 K
文摘
This paper introduces a concept of lattice-theoretic contexts as well as their concept lattices. A lattice-theoretic context is a triple (G, M, I) with two complete lattices G, M and their Galois ideal I. A lattice-theoretic context and its concept lattice are a common generalization of classical FCA, Pócs’s formal fuzzy context, one-sided concept lattices, generalized concept lattices and L-fuzzy concept lattices (with hedges). When the lattices G, M are completely distributive, a reduction of the relation I in the lattice-theoretic context (G, M, I) can be obtained. Related algorithms to construct concept lattices of L-fuzzy contexts considered as lattice-theoretic contexts are presented. In the case of L being a completely distributive lattice, we can reduce the number of elements (objects or/and attributes) before computing the whole concept lattice. Then the related algorithm has lower complexity.