Characterizations of monotone right continuous functions which generate associative functions

被引：3
|
作者：
Zhang, Yun-Mao [1 ]
Wang, Xue-ping [1 ]
机构：
[1] Sichuan Normal Univ, Sch Math Sci, Chengdu 610066, Sichuan, Peoples R China
来源：
FUZZY SETS AND SYSTEMS | 2024年 / 477卷
基金：
中国国家自然科学基金;
关键词：
Associative function; Right continuous function; Pseudo-inverse; Semigroup; Triangular norm; TRIANGULAR NORMS; ADDITIVE GENERATORS;
D O I：
10.1016/j.fss.2023.108799
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Associativity of a two-place function T : [0, 1](2)->[0, 1] defined by T(x, y) = f((-1))(T*(f(x), f(y))) where T* : [0, 1](2) -> [0, 1] is an associative function with neutral element in [0, 1], f : [0, 1] -> [0, 1] is a monotone right continuous function and f((-1)) : [0, 1] -> [0, 1] is the pseudo-inverse of f depends only on properties of the range of f. The necessary and sufficient conditions for the T to be associative are presented by applying the properties of the monotone right continuous function f.
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页数：14
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