论文标题
通过间隔关系分解晶格
Factorizing Lattices by Interval Relations
论文作者
论文摘要
这项工作调查了有限晶格的分解以溶解所选间隔，同时保留剩余的顺序结构。我们研究了如何将全面的一致关系和完全的宽容关系用于此目的，并回答找到这些关系中最好的问题以将给定间隔插入生成的因子晶格中的问题。为了克服基于这些关系的分解的局限性，我们引入了一个新的晶格分解，使有限晶格的选定不相交间隔内置。为此，我们提出了一个间隔关系来产生这种分解。为了获得晶格而不是任意有序集，我们将这种方法限制为所谓的纯间隔。在我们的研究中，我们将利用正式概念分析（FCA）中的方法。我们还将通过在正式环境中通过一组间隔引入发病率关系的丰富来提供新的FCA结构，以调查上下文方面的晶格生成间隔关系的方法。
This work investigates the factorization of finite lattices to implode selected intervals while preserving the remaining order structure. We examine how complete congruence relations and complete tolerance relations can be utilized for this purpose and answer the question of finding the finest of those relations to implode a given interval in the generated factor lattice. To overcome the limitations of the factorization based on those relations, we introduce a new lattice factorization that enables the imploding of selected disjoint intervals of a finite lattice. To this end, we propose an interval relation that generates this factorization. To obtain lattices rather than arbitrary ordered sets, we restrict this approach to so-called pure intervals. For our study, we will make use of methods from Formal Concept Analysis (FCA). We will also provide a new FCA construction by introducing the enrichment of an incidence relation by a set of intervals in a formal context, to investigate the approach for lattice-generating interval relations on the context side.
