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.
Cite
@article{arxiv.1212.2484,
title = {Decision Making with Partially Consonant Belief Functions},
author = {Phan H. Giang and Prakash P. Shenoy},
journal= {arXiv preprint arXiv:1212.2484},
year = {2012}
}
Comments
Appears in Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI2003)