Decision with Dempster-Shafer belief functions: Decision under ignorance and sequential consistency |
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Authors: | Phan H Giang |
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Institution: | George Mason University, 4400 University Dr., Fairfax, VA 22030, USA |
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Abstract: | This paper examines proposals for decision making with Dempster-Shafer belief functions from the perspectives of requirements for rational decision under ignorance and sequential consistency. The focus is on the proposals by Jaffray & Wakker and Giang & Shenoy applied for partially consonant belief functions. We formalize the concept of sequential consistency of an evaluation model and prove results about sequential consistency of Jaffray-Wakker’s model and Giang-Shenoy’s model under various conditions. We demonstrate that the often neglected assumption about two-stage resolution of uncertainty used in Jaffray-Wakker’s model actually disambiguates the foci of a belief function, and therefore, makes it a partially consonant on the extended state space. |
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Keywords: | Decision theory Belief function Partially consonant Ignorance Sequential consistency |
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