BELIEF FUNCTIONS AND THE TRANSFERABLE BELIEF MODEL

Belief functions have been proposed for modeling someone's de- grees of belief. They provide alternatives to the models based on probability functions or on possibility functions. There are several interpretations of belief functions: the lower probabilities model, Dempster's model, the hint model, the probability of modal propositions model, the transferable belief model. All these models are unfortunately clustered under the generic name of Dempster{ Shafer theory, which hides their dierences and explains most of the confusion and errors that appear in the literature.

[1]  Philippe Smets,et al.  Information Content of an Evidence , 1983, Int. J. Man Mach. Stud..

[2]  J. Kohlas,et al.  A Mathematical Theory of Hints: An Approach to the Dempster-Shafer Theory of Evidence , 1995 .

[3]  Ronald R. Yager,et al.  The entailment principle for dempster—shafer granules , 1986, Int. J. Intell. Syst..

[4]  Edward H. Shortliffe,et al.  The Dempster-Shafer theory of evidence , 1990 .

[5]  Philippe Smets.  Probability of Provability and Belief Functions , 1999 .

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

[7]  Serafín Moral,et al.  On the concept of possibility-probability consistency , 1987 .

[8]  Didier Dubois,et al.  Focusing versus updating in belief function theory , 1994 .

[9]  Philippe Smets,et al.  The Transferable Belief Model for Quantified Belief Representation , 1998 .

[10]  G. Klir,et al.  Uncertainty-based information: Elements of generalized information theory (studies in fuzziness and soft computing). , 1998 .

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

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

[13]  Serafín Moral Callejón.  Información difusa: relaciones entre probabilidad y posibilidad , 1985 .

[14]  Philippe Smets,et al.  Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem , 1993, Int. J. Approx. Reason..

[15]  Petr Hájek,et al.  On Belief Functions , 1992, Advanced Topics in Artificial Intelligence.

[16]  Cedric A. B. Smith,et al.  Consistency in Statistical Inference and Decision , 1961 .

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

[18]  L. Stein,et al.  Probability and the Weighing of Evidence , 1950 .

[19]  Philippe Smets,et al.  The Nature of the Unnormalized Beliefs Encountered in the Transferable Belief Model , 1992, UAI.

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

[21]  Nic Wilson,et al.  Decision-Making with Belief Functions and Pignistic Probabilities , 1993, ECSQARU.

[22]  G. Klir.  Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like? , 1987 .

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

[24]  James C. Bezdek,et al.  Uncertainty measures for evidential reasoning II: A new measure of total uncertainty , 1993, Int. J. Approx. Reason..

[25]  La représentation de la croyance , 1987 .

[26]  James C. Bezdek,et al.  Uncertainty measures for evidential reasoning I: A review , 1992, Int. J. Approx. Reason..

[27]  E. Ruspini.  The Logical Foundations of Evidential Reasoning (revised) , 1987 .

[28]  S. Moral,et al.  On the concept of possibility-probability consistency , 1987 .

[29]  I. Graham.  Non-standard logics for automated reasoning , 1990 .

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

[31]  Philippe Smets.  The alpha-junctions: Combination Operators Applicable to Belief Functions , 1997, ECSQARU-FAPR.

[32]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[33]  G. Shafer.  A Theory of Statistical Evidence , 1976 .

[34]  A. Tversky,et al.  Languages and designs for probability , 1985 .

[35]  Ronald Fagin,et al.  Two Views of Belief: Belief as Generalized Probability and Belief as Evidence , 1992, Artif. Intell..

[36]  Didier Dubois,et al.  On the unicity of dempster rule of combination , 1986, Int. J. Intell. Syst..

[37]  Frank Klawonn,et al.  The Dynamic of Belief in the Transferable Belief Model and Specialization-Generalization Matrices , 1992, UAI.

[38]  Bruce G. Buchanan,et al.  The MYCIN Experiments of the Stanford Heuristic Programming Project , 1985 .

[39]  Yen-Teh Hsia.  Characterizing Belief with Minimum Commitment , 1991, IJCAI.

[40]  Judea Pearl,et al.  Reasoning with belief functions: An analysis of compatibility , 1990, Int. J. Approx. Reason..

[41]  Didier Dubois,et al.  The principle of minimum specificity as a basis for evidential reasoning , 1986, IPMU.

[42]  Philippe Smets,et al.  What is Dempster-Shafer's model? , 1994 .

[43]  R. Kruse,et al.  SPECIALIZATION—A NEW CONCEPT FOR UNCERTAINTY HANDLING WITH BELIEF FUNCTIONS , 1990 .