Directional and Ordered Directional Monotonicity of Mixture Functions

In this contribution, we discuss the concepts of so-called fusion functions, pre-aggregation functions and their directional and ordered directional monotonicity in the context of mixture functions. Mixture functions represent a special class of weighted averaging functions whose weights are determined by continuous weighting functions which depend on the input values. They need not be monotone, in general. If they are monotone increasing, they also belong to the important class of aggregation functions. If the are directionally monotone, they belong to the class of pre-aggregation functions.

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