Ordinal sums of quasi-overlap functions on bounded lattices

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-09-10 DOI:10.1016/j.fss.2025.109581

Jun Geng , Yutong Zhang , Junsheng Qiao

引用次数: 0

Abstract

In this paper, we originally explore the ordinal sum equations of quasi-overlap functions on bounded lattices taking into account the potential incomparability of elements within the lattice structures. First, we give the ordinal sum of quasi-overlap functions on bounded lattices with more summands including finite and infinite cases, and establish the corresponding characterization theorems. Subsequently, we study another ordinal sum of quasi-overlap functions still being a quasi-overlap function on more general lattice structures. Finally, we investigate features of the underlying lattices to make the ordinal sum retains key properties of the given quasi-overlap functions. Additionally, some illustrative examples are provided for clarity.

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有界格上拟重叠函数的序数和

本文首先研究了有界晶格上的拟重叠函数的序和方程，考虑了晶格结构中元素的潜在不可比性。首先给出了包含有限和无限两种情况的多和有界格上拟重叠函数的序数和，并建立了相应的表征定理。随后，我们研究了在更一般的晶格结构上仍然是拟重叠函数的另一个序和。最后，我们研究了底层格的特征，使序和保留了给定拟重叠函数的关键性质。此外，为了清晰起见，还提供了一些说明性示例。

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.