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arXiv · 1212.2484

Decision Making with Partially Consonant Belief Functions

Phan H. Giang·Prakash P. Shenoy
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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.

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Phan H. Giang, Prakash P. Shenoy. 2012-10-19. Decision Making with Partially Consonant Belief Functions. https://arxiv.org/abs/1212.2484

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