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arXiv · 2506.18944

Characterizations of monotone right continuous functions which generate associative functions

Yun-Mao Zhang·Xue-ping Wang
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Abstract

Associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(T^*(f(x),f(y)))$ where $T^*:[0,1]^2\rightarrow[0,1]$ is an associative function with neutral element in $[0,1]$, $f: [0,1]\rightarrow [0,1]$ is a monotone right continuous function and $f^{(-1)}:[0,1]\rightarrow[0,1]$ 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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Yun-Mao Zhang, Xue-ping Wang. 2025-06-23. Characterizations of monotone right continuous functions which generate associative functions. https://arxiv.org/abs/2506.18944

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