Constructing ordinal sums of right and left semi-overlap functions on complete lattices

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-04-07 DOI:10.1016/j.fss.2025.109398

Jing Lu, Bin Zhao

引用次数: 0

Abstract

In this paper, the ordinal sum of a family of given right (resp., left) semi-overlap functions on subintervals in a complete lattice is constructed whenever the subintervals are pairwise non-overlapped and all the endpoints of the subintervals compose a chain. More precisely, we prove that the ordinal sum of right (resp., left) semi-overlap functions on subintervals in a complete lattice (resp., frame) is a right (resp., left) semi-overlap function on the sub-lattice consisting of all elements that are comparable with the endpoints of all subintervals, under the assumption that the least element of the complete lattice (resp., frame) is a prime element. And then, we extend the above right (resp., left) semi-overlap function on the sub-lattice to the whole complete lattice (resp., frame) with additional conditions by using the interior (resp., closure) operator.

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构造完备格上左右半重叠函数的序和

本文讨论了给定权族的序数和。当子区间成对不重叠且子区间的所有端点构成一条链时，构造完备格中子区间上的半重叠函数。更确切地说，我们证明了权（权）的序数和。，左)在完全格的子区间上的半重叠函数。（帧）是一种权利。，左)在由与所有子区间的端点可比较的所有元素组成的子格上的半重叠函数，假设完整格的最小元素(p。（frame）是一个素数元素。然后，我们将上面的右表达式展开。（左）子格到整个完备格的半重叠函数。，框架)，并通过使用内部(参见。（闭包）操作符。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.