Curve-based monotonicity: a generalization of directional monotonicity. Issue 5 (4th July 2019) - Roldán-López-de-Hierro, Antonio F.; Sesma-Sara, Mikel; Špirková, Jana; Lafuente, Julio; Pradera, Ana; Mesiar, Radko; Bustince, Humberto
ABSTRACT: In this work we propose a generalization of the notion of directional monotonicity. Instead of considering increasingness or decreasingness along rays, we allow more general paths defined by curves in the n -dimensional space. These considerations lead us to the notion of α -monotonicity, where α is the corresponding curve. We study several theoretical properties of α -monotonicity and relate it to other notions of monotonicity, such as weak monotonicity and directional monotonicity.