The aim of this work is to study the conditional distributivity given by the following functional equation: $$\begin{aligned} F(x,U(y,z))=U(F(x,y),F(x,z)),\ \ x,y,z\in [0,1],\ \ 0 <1 \end{aligned}$$ where F is a nullnorm and U is a uninorm. The paper discusses one case: F is continuous and \(U\in \mathcal {U}_{\max }\) (\(\mathcal {U}_{\min }\)) with continuous underlying operators.

中文翻译：

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零范数对单数的条件分布

这项工作的目的是研究以下功能方程式给出的条件分布：$$ \ begin {aligned} F（x，U（y，z））= U（F（x，y），F（x， z）），\ \ x，y，z \ in [0,1]，\ \ 0 <1 \ end {aligned} $$ 其中 F 是零范数，而 U 是单范数。本文讨论了一种情况： F 是连续的，并且\（U \ in \ mathcal {U} _ {\ max} \）（\（\ mathcal {U} _ {\ min} \））具有连续的基础运算符。