Input Importance in Aggregation Theory by Means of Dependence Stochastic Orders

Aggregation functions are usually used to summarize the information from different inputs into a unique value. Depending on the structure of the aggregation function and the behavior of the initial data, there are inputs that have a larger impact in the result of the aggregation. From a probabilistic approach, such an importance can be identified as the positive dependence between the input and the output. In this paper, sufficient conditions for the stochastic ordering with respect to positive dependence stochastic orders between bivariate random vectors consist-ing of an input and the output of aggregation functions are provided. In particular, quasi-arithmetic means and some OWA operators are con-sidered, using as ordering the supermodular and concordance stochastic orders.