Overlap and grouping functions, as two new classes of special binary aggregation functions, have been investigated by several authors for applications in image processing, decision making, classification, and fuzzy community detection problems. On the other hand, after Aczél studied the distributive law between two operations, the distributive laws among particular binary aggregation functions become an interesting and natural research area. In this paper, we continue to discuss this topic for uninorms and overlap and grouping functions. First, we give some basic properties for the distributive law of uninorms over overlap functions. Second, we study this distributive law when the uninorms belong to one of the usual classes (e.g., $\mathcal {U}_{\min }$, $\mathcal {U}_{\max }$, the family of idempotent uninorms, representable uninorms or uninorms continuous on $]0,1[^2$). Finally, we investigate the distributive law of uninorms over grouping functions by an analogous way.

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关于单范数重叠和分组函数的分配规律

重叠和分组函数作为两类新的特殊二元聚合函数，已经被几位作者研究在图像处理、决策制定、分类和模糊社区检测问题中的应用。另一方面，在 Aczél 研究了两个运算之间的分配律后，特定二元聚合函数之间的分配律成为一个有趣且自然的研究领域。在本文中，我们将继续讨论单范式以及重叠和分组函数的这一主题。首先，我们给出了重叠函数上单范式分配律的一些基本性质。其次，当单项属于一个通常的类（例如，$\mathcal {U}_{\min }$, $\mathcal {U}_{\max }$, 幂等单项、可表示单项或在上连续的单项的族 $]0,1[^2$）。最后，我们通过类似的方式研究了分组函数上的单项分布规律。