论文标题
有限格子的三角形规范
Triangular norms on bounded trellises
论文作者
论文摘要
在本文中，我们介绍了有界伪有序集的T-norm的概念，尤其是在有限的格子（也称为弱关联晶格）上，并提供了一些基本示例。放弃传递性的影响是相当大的：在适当的有限格子上，遇见操作不是T-norm，并且实际上可能没有或什至多个最大T-norms。我们提供了一种通用的施工方法，该方法允许在给定的$ \ MED $ -SEMI-TRELLIS的内部范围内将T-Norm扩展到整个$ \ MEED $ -SEMI-TRELLIS。另外，我们详细讨论了基于特定内部范围的该方法的实例化，即给定格子的一组右传递元素的有限亚细胞。我们要特别注意有限的伪链和模块化的格子。
In this paper, we introduce the notion of a t-norm on bounded pseudo-ordered sets and in particular on bounded trellises (also known as weakly associative lattices), and provide some basic examples. The impact of abandoning transitivity is considerable: on a proper bounded trellis, the meet operation is not a t-norm, and there might actually exist no or even multiple maximal t-norms. We provide a first generic construction method that allows to extend a t-norm on an interior range of a given $\meet$-semi-trellis to the entire $\meet$-semi-trellis. Also, we discuss at length an instantiation of this method based on a particular interior range, namely a finite sub-trellis of the set of right-transitive elements of a given trellis. We pay specific attention to bounded pseudo-chains and modular trellises.
