Continuous Archimedean t-norms and their bounds

V. Marko; R. Mesiar

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Continuous Archimedean t-norms and their bounds

机译：连续的阿基米德t范数及其范围

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摘要

Upper and lower bounds in the class of continuous Archimedean t-norms are studied. The existence of strict (nilpotent) bounds of finite families of strict (nilpotent) t-norms is shown in a constructive way, based on the additive generators of the corresponding t-norms. In general, a nilpotent lower bound and a strict upper bound of a finite system of any continuous Archimedean t-norms can be found. Some examples and some applications are given. By the duality, similar results for Bounds of continuous Archimedean t-conorms can be derived.

机译：研究了连续阿基米德t模中的上下界。基于对应的t模的加性生成器，以构造性方式显示了严格的（幂等）t模的有限族的严格（幂等）界。通常，可以找到任何连续的阿基米德t模的有限系统的幂等下界和严格上界。给出了一些例子和一些应用。通过对偶性，可以得出连续的阿基米德t-定理界的相似结果。

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来源
《Fuzzy sets and systems》 |2001年第2期|p.183-190|共8页
作者
V. Marko; R. Mesiar;
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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类模糊数学;
关键词
Additive generator; Nilpotnt t-norm; Strict t-norm;

机译：添加剂发生器;零幂t范数;严格的t范数;

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专利

1. On the determination of left-continuous t-norms and continuous archimedean t-norms on some segments [J] . Sándor Jenei Aequationes mathematicae . 2005,第1a2期

机译：关于确定某些段上的左连续t范数和连续阿基米德t范数的确定
2. On the determination of left-continuous t-norms and continuous archimedean t-norms on some segments [J] . Sándor Jenei Aequationes mathematicae . 2005,第1a2期

机译：关于确定某些段上的左连续t范数和连续阿基米德t范数的确定
3. Q-Rung Orthopair Fuzzy Integrals in the Frame of Continuous Archimedean T-Norms and T-Conorms and Their Application [J] . Ai Zhenghai, Xu Zeshui, Yager Ronald R., IEEE Transactions on Fuzzy Systems . 2021,第5期

机译：Q-rung orthopair模糊集成在连续的Archimedean T-Norms和T-Conorms及其应用的框架中
4. On the distributive equation of implication based on a continuous t-norm and a continuous Archimedean t-conorm [C] . Qin Feng, Yang Ping-Chong 2011 4th International Conference on Biomedical Engineering and Informatics . 2011

机译：基于连续t-范数和连续阿基米德t-conorm的蕴涵分布方程
5. Bounded Archimedean f-rings. [D] . Fawaz, Zahi. 2016

机译：有界的阿基米德F环。
6. On the Logic of Left-Continuous t-Norms and Right-Continuous t-Conorms [O] . Lluís Godo, Martín Sócola-Ramos, Francesc Esteva -1

机译：关于左连续t范和右连续t范式的逻辑
7. A generalization of the Mulholland inequality for continuous Archimedean t-norms [O] . Saminger-Platz Susanne, De Baets Bernard, De Meyer Hans 2008

机译：连续阿基米德t范数的Mulholland不等式的推广

Continuous Archimedean t-norms and their bounds

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