Interval-valued pre-aggregation functions - a study of directional monotonicity of interval-valued functions.

Pre-aggregation functions have extended the framework of valid functions to fuse data with respect to aggregation functions, in the sense that the monotonicity requirements are relaxed. Moreover, this class of functions has proven to be useful in classification problems. In this work we present the concept of directional monotonicity for interval-valued functions and use it to define the concept of interval-valued pre-aggregation functions. Additionally, we present some relevant properties of directionally monotone interval-valued functions and a method to construct interval-valued pre-aggregation functions from standard pre-aggregation functions.