Decision Making with Partially Consonant Belief Functions

Abstract

This paper studies decision making for Walley’s partially consonant belief functions (pcb). In a pcb, the set of foci are partitioned. Within each partition, foci are nested. The pcb class includes probability and possibility functions as extreme cases. We adopt an axiomatic system, similar in spirit to von Neumann and Morgenstern’s axioms for preferences leading to the linear utility theory, for a preference relation on pcb lotteries. We prove a representation theorem for this preference relation. Utility for a pcb lottery is a combination of linear utility for probabilistic lottery and binary utility for possibilistic lottery.