Decision Making with Partially Consonant Belief Functions
This provides a theoretical framework for decision-making in AI and economics, but it is incremental as it builds on existing axiomatic approaches.
The paper tackles decision making under uncertainty for partially consonant belief functions, proving a representation theorem that combines linear utility for probabilistic lotteries and binary utility for possibilistic lotteries.
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, the foci are nested. The pcb class includes probability functions and possibility functions as extreme cases. Unlike earlier proposals for a decision theory with belief functions, we employ an axiomatic approach. We adopt an axiom system similar in spirit to von Neumann - Morgenstern's linear utility theory for a preference relation on pcb lotteries. We prove a representation theorem for this relation. Utility for a pcb lottery is a combination of linear utility for probabilistic lottery and binary utility for possibilistic lottery.