Abstract Our investigations are motivated by the fact uninorms as mixed aggregation operations on the unit interval have been widely used in fuzzy set theory. This paper is mainly to characterize the inner structure of uninorms with continuous underlying operators given by ordinal sums, and then presents some of their properties. To be specific, for a uninorm, we describe the relations of its two arbitrary summands and characterize the structure on Cartesian products of its underlying intervals corresponding to those two summands mentioned previously (one in [ 0 , e ] and the other in [ e , 1 ] , where e is the neutral element of the uninorm). These results bring us a step closer to get the full structure of a uninorm with continuous underlying operators.

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关于具有连续基础运算符的单范式的说明

摘要 我们的研究是由单范式这一事实驱动的，因为单位区间上的混合聚合操作已广泛用于模糊集理论。本文主要是刻画由序数和给定的具有连续底层算子的单项的内部结构，然后给出它们的一些性质。具体来说，对于一个单项，我们描述了它的两个任意被加数的关系，并描述了对应于前面提到的那两个被加数（一个在 [ 0 , e ] 中，另一个在 [ e , 1 ] ，其中 e 是单范式的中性元素）。这些结果使我们更接近于获得具有连续底层运算符的单范式的完整结构。