Lower previsions induced by filter maps

We investigate under which conditions a transformation of an imprecise probability model of a certain type (coherent lower previsions, n  -monotone capacities, minitive measures) produces a model of the same type. We give a number of necessary and sufficient conditions, and study in detail a particular class of such transformations, called filter maps. These maps include as particular models multi-valued mappings as well as other models of interest within imprecise probability theory, and can be linked to filters of sets and {0,1}$\{0,1\}$-valued lower probabilities.