Abstract Overlap and grouping functions as two kinds of special continuous, commutative aggregation functions have wide applications in image processing and classification. Modularity conditions between the class of overlap (grouping) functions satisfying O ( 1 , e ) = e ( G ( 0 , e ) = e ) and special classes of uninorms, and those of another special class of overlap (grouping) functions over nullnorms have been studied in [49] . In this paper we extend these results to any overlap (grouping) function. Moreover, we study the modularity conditions between overlap (grouping) functions and uni-nullnorms (null-uninorms), which are the generalization of uninorms (nullnorms).

中文翻译：

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重叠（分组）函数和 uni-nullnorm 或 null-uninorm 之间的模块化条件

摘要 重叠和分组函数作为两种特殊的连续、可交换的聚合函数，在图像处理和分类中有着广泛的应用。满足 O ( 1 , e ) = e ( G ( 0 , e ) = e ) 的重叠（分组）函数类和特殊的单范数类之间的模块化条件，以及另一个特殊类重叠（分组）函数在零范数上的模块化条件在[49]中进行了研究。在本文中，我们将这些结果扩展到任何重叠（分组）函数。此外，我们研究了重叠（分组）函数和单零范数（null-uninorms）之间的模块化条件，它们是单范数（nullnorms）的推广。