论文标题
两个二进制操作的序数总和是有限晶格的T-norm
Ordinal sum of two binary operations being a t-norm on bounded lattice
论文作者
论文摘要
有界晶格上的T-norm的序数总和已用于构建其他T-norms。但是，在有界晶格的固定子间隔上定义的二进制操作（不一定是T-norms）的序数总和可能不是T-norm。在本文中提出了一些必要和充分的条件，以确保在两个二元操作的有界晶格上的序数总和实际上是T-norm。特别是，此处介绍的结果为Ertuğrul和Yeşilyurt提出的开放问题提供了答案[有限晶格上的三角形规范的序数总和，Inf。 Sci。，517（2020）198-216]。
The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an ordinal sum of binary operations (not necessarily t-norms) defined on the fixed subintervals of a bounded lattice may not be a t-norm. Some necessary and sufficient conditions are presented in this paper for ensuring that an ordinal sum on a bounded lattice of two binary operations is, in fact, a t-norm. In particular, the results presented here provide an answer to an open problem put forward by Ertuğrul and Yeşilyurt [Ordinal sums of triangular norms on bounded lattices, Inf. Sci., 517 (2020) 198-216].
