Approximation of the functional equation I(x, I(x, y)) = I(x, y)
物理
数学物理
数学
组合数学
作者
Songsong Dai
出处
期刊:Journal of Intelligent and Fuzzy Systems [IOS Press] 日期:2024-02-23卷期号:: 1-8
标识
DOI:10.3233/jifs-233435
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.