A Defect in Dempster-Shafer Theory

By analyzing the relationships among chance, weight of evidence and degree of belief, we show that the assertion "probability functions are special cases of belief functions" and the assertion "Dempster's rule can be used to combine belief functions based on distinct bodies of evidence" together lead to an inconsistency in Dempster-Shafer theory. To solve this problem, we must reject some fundamental postulates of the theory. We introduce a new approach for uncertainty management that shares many intuitive ideas with D-S theory, while avoiding this problem.

[1]  Pei Wang,et al.  Belief Revision in Probability Theory , 1993, UAI.

[2]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[3]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[4]  Pei Wang.  From inheritance relation to nonaxiomatic logic , 1994, Int. J. Approx. Reason..

[5]  Henry E. Kyburg,et al.  Bayesian and Non-Bayesian Evidential Updating , 1987, Artificial Intelligence.

[6]  Philippe Smets.  The transferable belief model and other interpretations of Dempster-Shafer's model , 1990, UAI.

[7]  Glenn Shafer,et al.  Perspectives on the theory and practice of belief functions , 1990, Int. J. Approx. Reason..

[8]  Ronald Fagin,et al.  A new approach to updating beliefs , 1990, UAI.

[9]  Frans Voorbraak,et al.  On the Justification of Dempster's Rule of Combination , 1988, Artif. Intell..

[10]  Nic Wilson.  The combination of belief: When and how fast? , 1992, Int. J. Approx. Reason..

[11]  Nic Wilson.  The Assumptions Behind Dempster's Rule , 1993, UAI.

[12]  Philippe Smets,et al.  Belief Induced by the Partial Knowledge of the Probabilities , 1994, UAI.

[13]  Philippe Smets,et al.  The Combination of Evidence in the Transferable Belief Model , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Glenn Shafer,et al.  Languages and Designs for Probability Judgment , 1985, Cogn. Sci..

[15]  Didier Dubois,et al.  Updating with belief functions, ordinal conditional functions and possibility measures , 1990, UAI.

[16]  Pei Wang.  From Inheritance Relation to Non-Axiomatic Logic , 1994 .

[17]  Didier Dubois,et al.  Evidence, knowledge, and belief functions , 1992, Int. J. Approx. Reason..

[18]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.