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arXiv · 2601.10756

Monotone functions that generate conditionally cancellative triangular subnorms

Meng Chen·Xue-ping Wang
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Abstract

Let a function $F: [0,1]^2\rightarrow [0,1]$ be given by $F(x,y)= f^{(-1)}(T(f(x), f(y)))$ where $f :[0,1]\rightarrow [0,1]$ is a monotone function, $f^{(-1)}$ is the pseudo-inverse of $f$ and $T$ is a triangular norm. This article characterizes the monotone function $f$ satisfying that the function $F$ is a conditionally cancellative triangular subnorm completely. It finally answers an open problem posed by Mesiarov\'{a}.

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Meng Chen, Xue-ping Wang. 2026-01-14. Monotone functions that generate conditionally cancellative triangular subnorms. https://arxiv.org/abs/2601.10756

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