TY - JOUR

T1 - Dempster's rule of combination

AU - Shafer, Glenn

N1 - Funding Information:
Some of the work in this paper was done while the author was supported by a National Science Foundation Graduate Fellowship. The work was completed with support from the General Research Fund of the University of Kansas , allocations # 3991-x038 and # 3315-x038 .
Publisher Copyright:
© 2016 Elsevier Inc.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - The theory of belief functions is a generalization of probability theory; a belief function is a set function more general than a probability measure but whose values can still be interpreted as degrees of belief. Dempster's rule of combination is a rule for combining two or more belief functions; when the belief functions combined are based on distinct or “independent” sources of evidence, the rule corresponds intuitively to the pooling of evidence. As a special case, the rule yields a rule of conditioning which generalizes the usual rule for conditioning probability measures. The rule of combination was studied extensively, but only in the case of finite sets of possibilities, in the author's monograph A Mathematical Theory of Evidence. The present paper describes the rule for general, possibly infinite, sets of possibilities. We show that the rule preserves the regularity conditions of continuity and condensability, and we investigate the two distinct generalizations of probabilistic independence which the rule suggests.

AB - The theory of belief functions is a generalization of probability theory; a belief function is a set function more general than a probability measure but whose values can still be interpreted as degrees of belief. Dempster's rule of combination is a rule for combining two or more belief functions; when the belief functions combined are based on distinct or “independent” sources of evidence, the rule corresponds intuitively to the pooling of evidence. As a special case, the rule yields a rule of conditioning which generalizes the usual rule for conditioning probability measures. The rule of combination was studied extensively, but only in the case of finite sets of possibilities, in the author's monograph A Mathematical Theory of Evidence. The present paper describes the rule for general, possibly infinite, sets of possibilities. We show that the rule preserves the regularity conditions of continuity and condensability, and we investigate the two distinct generalizations of probabilistic independence which the rule suggests.

KW - Belief function

KW - Cognitive independence

KW - Conditioning

KW - Dempster's rule

KW - Evidential independence

KW - Upper probabilities

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U2 - 10.1016/j.ijar.2015.12.009

DO - 10.1016/j.ijar.2015.12.009

M3 - Article

AN - SCOPUS:84955262690

SN - 0888-613X

VL - 79

SP - 26

EP - 40

JO - International Journal of Approximate Reasoning

JF - International Journal of Approximate Reasoning

ER -