Overlap functions are aggregation functions that express the overlapping degree between two values. They have been used both as a conjunction in several practical problems (e.g., image processing and decision making), and to generate overlap indices between two fuzzy sets, which can be used to construct fuzzy confidence values to be applied in fuzzy rule based classification systems. Some generalizations of overlap functions were recently proposed, such as n-dimensional and general overlap functions, which allowed their application in n-dimensional problems. More recently, the concept of interval-valued overlap functions was presented, mainly to deal with uncertainty in providing membership functions. In this paper, we introduce: (i) the concept of n-dimensional interval-valued overlap functions, studying their representability, (ii) the definition of general interval-valued overlap functions, providing their characterization and some construction methods. Moreover, we also define the concept of interval-valued overlap index, as well as some constructing methods. In addition, we show an illustrative example where those new concepts are applied.

重叠函数是表示两个值之间重叠程度的聚合函数。它们已被用作一些实际问题（例如，图像处理和决策）中的结合，并已在两个模糊集之间生成重叠索引，可用于构造模糊置信度值以应用于基于模糊规则的分类系统。最近提出了重叠函数的一些概括，例如n维和通用重叠函数，这使得它们可以应用在n维问题中。最近，提出了区间值重叠函数的概念，主要是为了解决提供隶属函数时的不确定性。在本文中，我们介绍：（i）n维间隔值重叠函数的概念，研究其可表示性，（ii）定义一般的区间值重叠函数，并提供其特征和一些构造方法。此外，我们还定义了间隔值重叠索引的概念以及一些构造方法。另外，我们展示了一个应用这些新概念的说明性示例。