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, 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.

Appears in Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI2003)

References in corpus (1)

• Statistical Decisions Using Likelihood Information Without Prior Probabilities

Cited by in corpus (2)

• Axiomatic Foundations for a Class of Generalized Expected Utility: Algebraic Expected Utility
• Decision Making for Symbolic Probability