Implementing belief function computations

This article discusses several implementation aspects for Dempster‐Shafer belief functions. The main objective is to propose an appropriate representation of mass functions and efficient data structures and algorithms for the two basic operations of combination and marginalization. © 2003 Wiley Periodicals, Inc.

[1]  Pierre Marquis,et al.  A Perspective on Knowledge Compilation , 2001, IJCAI.

[2]  Rolf Haenni,et al.  Resource bounded and anytime approximation of belief function computations , 2002, Int. J. Approx. Reason..

[3]  Michael Clarke,et al.  Symbolic and Quantitative Approaches to Reasoning and Uncertainty , 1991, Lecture Notes in Computer Science.

[4]  Prakash P. Shenoy,et al.  Binary join trees for computing marginals in the Shenoy-Shafer architecture , 1997, Int. J. Approx. Reason..

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

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

[7]  Rina Dechter,et al.  Bucket Elimination: A Unifying Framework for Reasoning , 1999, Artif. Intell..

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

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

[10]  Jürg Kohlas,et al.  Propositional Information Systems , 1999, J. Log. Comput..

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

[12]  Jürg Kohlas,et al.  Algorithms for uncertainty and defeasible reasoning , 2000 .

[13]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[14]  Jürg Kohlas,et al.  Handbook of Defeasible Reasoning and Uncertainty Management Systems , 2000 .

[15]  Norbert Lehmann,et al.  Argumentation systems and belief functions , 2001 .

[16]  John D. Lowrance,et al.  A Framework for Evidential-Reasoning Systems , 1990, AAAI.

[17]  Rolf Haenni,et al.  Probabilistic Argumentation Systems , 2003 .

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

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

[20]  David Thomas,et al.  The Art in Computer Programming , 2001 .

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

[22]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[23]  Detlef D. Nauck Fuzzy data analysis with NEFCLASS , 2003, Int. J. Approx. Reason..

[24]  Glenn Shafer,et al.  Readings in Uncertain Reasoning , 1990 .

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

[26]  Robert Kennes,et al.  Steps toward efficient implementation on Dempster-Shafer theory , 1994 .

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

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

[29]  Mathias Bauer Approximations for Decision Making in the Dempster-Shafer Theory of Evidence , 1996, UAI.

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

[31]  J. Kohlas,et al.  Information Algebras and Information Systems , 1996 .

[32]  Philippe Smets,et al.  The Transferable Belief Model , 1994, Artif. Intell..

[33]  Prakash P. Shenoy,et al.  Computation in Valuation Algebras , 2000 .

[34]  Prakash P. Shenoy,et al.  Valuation-based systems: a framework for managing uncertainty in expert systems , 1992 .

[35]  Donald E. Knuth,et al.  Sorting and Searching , 1973 .

[36]  Donald E. Knuth,et al.  The Art of Computer Programming, Vol. 3: Sorting and Searching , 1974 .

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

[38]  David Harmanec,et al.  Faithful Approximations of Belief Functions , 1999, UAI.

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