In this paper, we introduce the notion of ordered directionally monotone function as a type of function which allows monotonicity along different directions in different points. In particular, these functions take into account the ordinal size of the coordinates of the inputs in order to fuse them. We show several examples of these functions and we study their properties. Finally, we present an illustrative example of an application which justifies the introduction and the study of the concept of ordered directional monotonicity.

中文翻译：

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有序定向单调函数：理由与应用


在本文中，我们引入有序方向单调函数的概念，作为一种允许不同点沿不同方向单调性的函数。特别是，这些函数考虑输入坐标的序数大小以便融合它们。我们展示了这些函数的几个例子并研究了它们的属性。最后，我们提出了一个应用示例，证明了有序方向单调性概念的引入和研究的合理性。