Abstract Since Aczel studied the distributive law between two operations, the distributive laws among different binary aggregation functions become an interesting and vast research field. This paper is mainly devoted to solving the distributivity equations between 2-uninorms and overlap(grouping) functions, which are two classes of special aggregation functions found to possess wide applications in image processing, decision making, classification and fuzzy detection problems. We obtain the sufficient and necessary conditions of the distributivity equations between five classes of basic 2-uninorms and overlap(grouping) functions.

中文翻译：

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关于 2-uninorms 和重叠（分组）函数之间的分配律

摘要 由于Aczel研究了两个运算之间的分配规律，不同二元聚合函数之间的分配规律成为一个有趣而广阔的研究领域。本文主要致力于求解2-uninorms和overlap(grouping)函数之间的分布方程，这两类特殊的聚合函数被发现在图像处理、决策、分类和模糊检测问题中具有广泛的应用。我们得到了五类基本2-单范式和重叠（分组）函数之间分布方程的充要条件。