Abstract
Monotonicity is a fundamental property of aggregation. However not all means are monotone increasing. This chapter presents a weaker notion of directional monotonicity of averages. The robust estimators of location, mixture functions, Gini and Lehmer means, as well as density based means and medians are treated in the framework of weak monotonicity. Cone monotonicity and monotonicity with respect to coalitions are introduced and discussed. The notion of directional monotonicity is presented and pre-aggregation functions are formalized.
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