交叉迁移的若干类生成隐含解的特征

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

Fuzzy Sets and Systems Pub Date : 2025-03-18 DOI:10.1016/j.fss.2025.109375

Tianlong Zhang , Kuanyun Zhu , Jingru Wang , Deng Pan

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引用次数: 0

摘要

本文主要讨论了群函数之间的交叉迁移性，以及由连续阿基米德t-正则的可加性生成的(g, min)-蕴涵和由可表示一致的广义可加性生成的h - 1蕴涵。此外，我们证明(g,min)-蕴涵和h- 1-蕴涵不属于已知的（S，N） -,R -,QL -，广义-h， h-生成，Yager的f-和g-蕴涵中的任何一类。特别地，我们利用群函数的乘法（加性）生成子和序和，群函数和模糊隐含子之间的分配律和收缩律，建立了群函数和若干特定类型的生成隐含子（即h-生成隐含子、k-生成隐含子、(g,min)-隐含子和h−1-隐含子）的交叉迁移性的一系列充要条件。并研究分组功能和生成的含义之间更广泛的联系。

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Characterizations of some classes of generated implication solutions to the cross-migrativity

This paper focuses on the cross-migrativity between grouping functions and the (g, min)-implications generated by additive generators of continuous Archimedean t-conorms and the

h^{- 1}

-implications introduced by generalized additive generators of representable uninorms. In addition, we show that (

g, \min

)-implications and

h^{- 1}

-implications do not belong to any of the classes known

(S, N) -, R -, Q L -

, generalized-h, h-generated, Yager's f- and g-implications. In particular, we establish a series of necessary and sufficient conditions for the cross-migrativity of the grouping functions and several particular types of generated implications (i.e., h-generated implications, k-generated implications, (

g, \min

)-implications and

h^{- 1}

-implications) by using the multiplicative (additive) generators and ordinal sums of grouping functions, the distributive laws and contraction law between grouping functions and fuzzy implications, and study a broader connection between grouping functions and generated implications.

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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.