ABSTRACT

The n-uninorms with continuous underlying t-norms and t-conorms are studied. We show that each 2-uninorm with continuous underlying functions can be expressed as an ordinal sum of a uninorm with continuous underlying functions (possibly also of a countable number of semigroups related to representable uninorms, continuous Archimedean t-norms, continuous Archimedean t-conorms and internal uninorms) and a 2-uninorm with continuous underlying functions such that $U^2(0,1)=z_1$ (possibly restricted to open or half-open unit square ${\left[0,1\right[}^2,$ ${\left]0,1\right]}^2$). Similar results are shown for n-uninorms with continuous underlying functions, where $n\in \mathbb{N},$ $n>2.$

摘要

所述Ñ连续底层叔规范和叔conorms -uninorms进行了研究。我们证明了具有连续基础函数的每个2范数可以表示为具有连续基础函数的单项的序数总和（可能还包括与可表示的单项，连续的阿基米德t范数，连续的阿基米德t弦图有关的无数个半群）和内部单项）和具有连续基础功能的2范数，例如${ü}^2（0，\mathrm{1个}）={ž}_{\mathrm{1个}}$ （可能仅限于开放式或半开放式单位正方形 ${\left[0，\mathrm{1个}\right[}^2，$ ${\left]0，\mathrm{1个}\right]}^2$）。对于具有连续基础函数的n个标准，显示了相似的结果，其中$ñ\in \mathbb{ñ}，$ $ñ>\mathrm{2。}$