Quasi-D-overlap functions: Construction and characterization

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

Fuzzy Sets and Systems Pub Date : 2024-09-24 DOI:10.1016/j.fss.2024.109138

Junsheng Qiao

引用次数: 0

Abstract

In this paper, we mainly consider the construction and characterization of so-called quasi-D-overlap functions, which are derived from D-overlap functions and irreducible quasi-D-overlap functions proposed by the author lately. The main contributions are: (i) it presents the concept of quasi-D-overlap functions and obtains construction manner of them by means of matrixes; (ii) it illustrates the relationship between quasi-D-overlap functions and 1-Lipschitz semi-quasi-overlap functions; (iii) it gives equivalent characterization of quasi-D-overlap functions and proper quasi-D-overlap functions by dint of matrixes, moreover, it obtains that the convex combination of quasi-D-overlap functions is also a quasi-D-overlap function.

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准 D 叠加函数：构造与特征

在本文中，我们主要考虑所谓准 D 叠加函数的构造和表征，它们是从 D 叠加函数和作者最近提出的不可还原准 D 叠加函数派生出来的。其主要贡献在于(i)提出了准 D 叠加函数的概念，并通过矩阵得到了准 D 叠加函数的构造方法；(ii)说明了准 D 叠加函数与 1Lipschitz 半准叠加函数之间的关系；(iii)通过矩阵给出了准 D 叠加函数和适当准 D 叠加函数的等价表征，并得到了准 D 叠加函数的凸组合也是准 D 叠加函数。

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.