The additive generators of t-norms and t-conorms on bounded lattices

被引：8

作者：

Sun, Xiang-Rong ^{[1
]}

Liu, Hua-Wen ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

来源：

FUZZY SETS AND SYSTEMS | 2021年 / 408卷

基金：

国家重点研发计划; 中国国家自然科学基金;

关键词：

Fuzzy connective; Triangular norm; Triangular conorm; Bounded lattice; Additive generator;

D O I：

10.1016/j.fss.2020.04.005

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we study the additive generators of t-norms and t-conorms on bounded lattices. They are not only good tools to construct but also crucial to studying the representations of t-norms and t-conorms. First we extend the classical additive generators theorem to the partially ordered cases by adding one more condition. Then we discuss some properties of these constructed t norms such as the Archimedean property, nilpotent elements, strict monotonicity, et cetera. Besides, we give a more convenient modification of our theorem on finite bounded lattices and several examples for a further step on the characteristics of the additive generators. (c) 2020 Elsevier B.V. All rights reserved.

引用

页码：13 / 25

页数：13

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