Approximation of the functional equation I(x, I(x, y)) = I(x, y)

被引：0
|
作者：
Dai S. [1 ]
机构：
[1] School of Electronics and Information Engineering, Taizhou University, Zhejiang, Taizhou
来源：
Journal of Intelligent and Fuzzy Systems | 2024年 / 46卷 / 04期
基金：
中国国家自然科学基金;
关键词：
(S; N)-implication; Functional equation; fuzzy implication; iterative boolean-like law;
D O I：
10.3233/JIFS-233435
中图分类号：
学科分类号：
摘要：
The well-known iterative boolean-like law a →(a → b) = a → b can be generalized to the functional equation I(x, I(x, y)) = I(x, y), where I is a fuzzy implication. In this paper, we discuss an approximation of the equation, I(x, I(x, y)) ≈ I(x, y), i.e., the law is approximately valid. Furthermore, we study the property of approximation preserving with respect to compositions of fuzzy implications. Finally, we give a necessary condition and a sufficient condition for the approximate equation of (S, N)-implications. © 2024 - IOS Press. All rights reserved.
引用
收藏
页码：9021 / 9028
页数：7
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