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Archimedean overlap functions: The ordinal sum and the cancellation, idempotency and limiting properties

机译：阿基米德重叠函数：序数和以及抵消，等幂和限制性质

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摘要

Overlap functions are a particular type of aggregation functions, given by increasing continuous commutative bivariate functions defined over the unit square, satisfying appropriate boundary conditions. Overlap functions are applied mainly in classification problems, image processing and in some problems of decision making based on some kind of fuzzy preference relations, in which the associativity property is not strongly required. Moreover, the class of overlap functions is reacher than the class of t-norms, concerning some properties like idempotency, homogeneity, and, mainly, the self-closedness feature with respect to the convex sum and the aggregation by generalized composition of overlap functions. This flexibility of overlap functions increases their applicability. The aim of this papers is to introduce the concept of Archimedean overlap functions, presenting a study about the cancellation, idempotency and limiting properties, and providing a characterization of such class of functions. The concept of ordinal sum of overlap functions is also introduced, providing constructing/representing methods of certain classes of overlap functions related to idempotency, cancellation, limiting and Archimedean properties.
机译：重叠函数是聚合函数的一种特殊类型，通过增加在单位平方上定义的连续可交换双变量函数来满足适当的边界条件。重叠函数主要应用于分类问题，图像处理以及基于某种模糊偏好关系的决策制定问题，在这些问题中，对关联性的要求不高。此外，重叠函数的类别比t范数的类别更广，涉及一些特性，如幂等性，同质性，以及主要是关于凸和的自封闭性特征和由重叠函数的广义组合引起的聚集。重叠功能的这种灵活性增加了它们的适用性。本文的目的是介绍阿基米德重叠函数的概念，对消除，幂等和极限性质进行研究，并提供此类函数的表征。还介绍了重叠函数的有序和的概念，提供了与幂等，抵消，限制和阿基米德性质有关的某些类别的重叠函数的构造/表示方法。

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