Affiliations:
School of Electronics and Information Engineering, Taizhou University, Taizhou, Zhejiang, China
Correspondence:
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Corresponding author. Songsong Dai, School of Electronics and information engineering, Taizhou University, Taizhou 318000, Zhejiang, China. E-mail: [email protected].
Abstract: 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.
