The n-uninorms with continuous underlying t-norms and t-conorms are characterized via the z-ordinal sum construction. We show that each n-uninorm with continuous underlying t-norms and t-conorms can be expressed as a z-ordinal sum of a countable number of Archimedean and idempotent semigroups with respect to the branching set $A\sim \{z_1,\dots ,z_{n-1}\}$, where the corresponding partial order has a tree structure.

中文翻译：

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通过z-有序求和构造来表征具有连续基础函数的n-范数

带有连续下标t范数和t范数的n范数通过z序和构造来表征。我们表明，每Ñ连续底层叔规范和叔conorms -uninorm可以表示为一个Ž阿基米德和幂等的半群的可数的总和-ordinal相对于所述支化组$\mathrm{一个}〜\{{ž}_{\mathrm{1个}}，\dots ，{ž}_{ñ-\mathrm{1个}}\}$，其中相应的偏序具有树结构。