Jeffrey-like rules of conditioning for the Dempster-Shafer theory of evidence
type: Item
instance of: scholarly article
title: Jeffrey-like rules of conditioning for the Dempster-Shafer theory of evidence
zbMATH Open document ID: 0665.62007
DOI: 10.1016/0888-613X(89)90003-0
published in: International Journal of Approximate Reasoning
publication date: 1989-01-01T00:00:00Z
review text: Jeffrey's rule of conditioning is a rule for changing an additive probability distribution when the human perception of new evidence is obtained. It is a generalization of the normative Bayesian inference. Shafer showed how Jeffrey's generalization of Bayes' rule of conditioning can be reinterpreted in terms of the theory of belief functions. But Shafer's approach is different from the normative Bayesian approach and is not a straight generalization of Jeffrey's rule. There are situations in which we need inference rules that may well provide a convenient generalization of Jeffrey's rule. Therefore we propose new rules of conditioning motivated by the work of \textit{D. Dubois} and \textit{H. Prade} [Int. J. Intell. Syst. 1, 133-142 (1986; Zbl 0641.68159)]. Although the weak and strong conditioning rules of Dubois and Prade are generalizations of Bayesian conditioning, they fail to yield Jeffrey's rule as a special case. Jeffrey's rule is a direct consequence of a special case of our conditioning rules. Three kinds of normalizations in the rules of conditioning are discussed.
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 68T05
Mathematics Subject Classification ID: 68T99
zbMATH DE Number: 4088700
zbMATH Keywords: theory of evidence
zbMATH Keywords: Dempster's rule of combination
zbMATH Keywords: upper and lower probabilities
zbMATH Keywords: Jeffrey's rule of conditioning
zbMATH Keywords: belief functions
zbMATH Keywords: new rules of conditioning
zbMATH Keywords: weak and strong conditioning
zbMATH Keywords: generalizations of Bayesian conditioning
zbMATH Keywords: normalizations
author: Hidetomo Ichihashi
author: Hideo Tanaka
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4088700