Algorithms for Dempster-Shafer Theory

The method of reasoning with uncertain information known as Dempster-Shafer theory arose from the reinterpretation and development of work of Arthur Dempster [Dempster, 1967; 1968] by Glenn Shafer in his book a mathematical theory of evidence [Shafer, 1976], and further publications e.g., [Shafer, 1981; 1990]. More recent variants of Dempster-Shafer theory include the Transferable Belief Model see e.g., [Smets, 1988; Smets and Keimes, 1994] and the Theory of Hints e.g., [Kohlas and Monney, 1995].

[1]  Prakash P. Shenoy,et al.  Propagating Belief Functions with Local Computations , 1986, IEEE Expert.

[2]  Hong Xu,et al.  Computing Marginals for Arbitrary Subsets from Marginal Representation in Markov Trees , 1995, Artif. Intell..

[3]  H. Thoma.  Factorization of belief functions , 1990 .

[4]  G. Shafer.  Lindley's Paradox , 1982 .

[5]  Jürg Kohlas,et al.  Fast-Division Architecture for Dempster-Shafer Belief Functions , 1997, ECSQARU-FAPR.

[6]  Ronald Fagin,et al.  Uncertainty, belief, and probability , 1989, IJCAI 1989.

[7]  Frans Voorbraak,et al.  A Computationally Efficient Approximation of Dempster-Shafer Theory , 1988, Int. J. Man Mach. Stud..

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

[9]  Didier Dubois,et al.  Consonant approximations of belief functions , 1990, Int. J. Approx. Reason..

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

[11]  Kathryn B. Laskey,et al.  Assumptions, Beliefs and Probabilities , 1989, Artif. Intell..

[12]  Hong Xu.  An Efficient Implementation of Belief Function Propagation , 1991, UAI.

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

[14]  Philippe Smets.  Non-standard logics for automated reasoning , 1988 .

[15]  Mathias Bauer,et al.  Approximation algorithms and decision making in the Dempster-Shafer theory of evidence - An empirical study , 1997, Int. J. Approx. Reason..

[16]  Gregory M. Provan,et al.  A logic-based analysis of Dempster-Shafer theory , 1990, Int. J. Approx. Reason..

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

[18]  Nic Wilson,et al.  Importance Sampling Monte-Carlo Algorithms for the Calculation of Dempster-Shafer Belief , 1996 .

[19]  Bjørnar Tessem,et al.  Approximations for Efficient Computation in the Theory of Evidence , 1993, Artif. Intell..

[20]  Glenn Shafer,et al.  Rejoinders to comments on "perspectives on the theory and practice of belief functions" , 1992, Int. J. Approx. Reason..

[21]  Wc Taylor,et al.  Special Issue , 2000, International Journal of Recent Technology and Engineering.

[22]  Larry Wasserman,et al.  Prior Envelopes Based on Belief Functions , 1990 .

[23]  V. Kreinovich,et al.  Monte-Carlo methods make Dempster-Shafer formalism feasible , 1994 .

[24]  Judea Pearl,et al.  Bayesian and belief-functions formalisms for evidential reasoning: a conceptual analysis , 1990 .

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

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

[27]  Nic Wilson,et al.  Markov Chain Monte-Carlo Algorithms for the Calculation of Dempster-Shafer Belief , 1994, AAAI.

[28]  Glenn Shafer,et al.  Implementing Dempster's Rule for Hierarchical Evidence , 1987, Artif. Intell..

[29]  J. Kacprzyk,et al.  Advances in the Dempster-Shafer theory of evidence , 1994 .

[30]  Jürg Kohlas,et al.  A Mathematical Theory of Hints , 1995 .

[31]  Nic Wilson,et al.  How much do you believe? , 1992, Int. J. Approx. Reason..

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

[33]  S. C. Sahasrabudhe,et al.  Bayesian Approximation and Invariance of Bayesian Belief Functions , 1995, ECSQARU.

[34]  Augustine Kong,et al.  Uncertain evidence and artificial analysis , 1990 .

[35]  Rolf Haenni,et al.  An Alternative to Outward Propagation for Dempster-Shafer Belief Functions , 1999, ESCQARU.

[36]  Ronald R. Yager,et al.  Uncertainty in Knowledge Bases , 1990, Lecture Notes in Computer Science.

[37]  Nic Wilson,et al.  Fast Markov Chain Algorithms for Calculating Dempster-Shafer Belief , 1996, ECAI.

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

[39]  Philippe Smets,et al.  Constructing the Pignistic Probability Function in a Context of Uncertainty , 1989, UAI.

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

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

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

[43]  Lotfi A. Zadeh,et al.  Review of A Mathematical Theory of Evidence , 1984 .

[44]  Prakash P. Shenoy,et al.  Axioms for probability and belief-function proagation , 1990, UAI.

[45]  Khaled Mellouli,et al.  Propagating belief functions in qualitative Markov trees , 1987, Int. J. Approx. Reason..

[46]  Nic Wilson,et al.  A Monte-Carlo Algorithm for Dempster-Shafer Belief , 1991, UAI.

[47]  Serafín Moral,et al.  A Monte Carlo Algorithm for Combining Dempster-Shafer Belief Based on Approximate Pre-computation , 1999, ESCQARU.

[48]  Madan M. Gupta,et al.  Conditional Logic in Expert Systems , 1991 .

[49]  Jeffrey A. Barnett,et al.  Computational Methods for a Mathematical Theory of Evidence , 1981, IJCAI.

[50]  Pekka Orponen,et al.  Dempster's Rule of Combination is #P-Complete , 1990, Artif. Intell..

[51]  Ronald R. Yager,et al.  Uncertainty in Intelligent Systems , 1993 .

[52]  Smets Ph.,et al.  Belief functions, Non-standard logics for automated reasoning , 1988 .

[53]  Thomas Kämpke.  About assessing and evaluating uncertain inferences within the theory of evidence , 1988, Decis. Support Syst..

[54]  Edward H. Shortliffe,et al.  A Method for Managing Evidential Reasoning in a Hierarchical Hypothesis Space , 1985, Artif. Intell..

[55]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .