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.
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Bustince et al. (2017) studied this question.
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