On the Dempster-Shafer evidence theory and non-hierarchical aggregation of belief structures

The Dempster's rule of combination is a widely used technique to integrate evidence collected from different sources. In this paper, it is shown that the values of certain functions defined on a family of belief structures decrease (by scale factors depending on the degree of conflict) when the belief structures are combined according to the Dempster's rule. Similar results also hold when an arbitrary belief structure is prioritized while computing the combination. Furthermore, the length of the belief-plausibility interval is decreased during a nonhierarchical aggregation of belief structures. Several types of inheritance networks are also proposed each of which allows considerable flexibility in the choice of prioritization.

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

[2]  R. Yager.  On the dempster-shafer framework and new combination rules , 1987, Inf. Sci..

[3]  Ronald P. S. Mahler,et al.  The modified Dempster-Shafer approach to classification , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[4]  Isabelle Bloch,et al.  Some aspects of Dempster-Shafer evidence theory for classification of multi-modality medical images taking partial volume effect into account , 1996, Pattern Recognit. Lett..

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

[6]  Prakash P. Shenoy,et al.  A valuation-based language for expert systems , 1989, Int. J. Approx. Reason..

[7]  Dennis M. Buede.  Shafer-Dempster and Bayesian reasoning: a response to 'Shafer-Dempster reasoning with applications to multisensor target identification systems' , 1988, IEEE Trans. Syst. Man Cybern..

[8]  George J. Klir,et al.  Uncertainty-Based Information , 1999 .

[9]  John D. Lowrance,et al.  Understanding evidential reasoning , 1992, Int. J. Approx. Reason..

[10]  A. Ramer.  Uniqueness of information measure in the theory of evidence , 1987 .

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

[12]  Pei Wang.  A Defect in Dempster-Shafer Theory , 1994, UAI.

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

[14]  Isabelle Bloch.  Information combination operators for data fusion: a comparative review with classification , 1996, IEEE Trans. Syst. Man Cybern. Part A.

[15]  Thomas M. Strat,et al.  Decision analysis using belief functions , 1990, Int. J. Approx. Reason..

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

[17]  Hans Jørgen Jacobsen,et al.  The product of capacities and belief functions , 1996 .

[18]  Qing Zhu,et al.  Fuzzy and Evidence Reasoning , 1995 .

[19]  Marvin Minsky,et al.  A framework for representing knowledge , 1974 .

[20]  P. L. Bogler,et al.  Shafer-dempster reasoning with applications to multisensor target identification systems , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

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

[22]  John D. Lowrance,et al.  Explaining evidential analyses , 1989, Int. J. Approx. Reason..

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

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

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

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

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

[28]  Thierry Denoeux,et al.  A k-nearest neighbor classification rule based on Dempster-Shafer theory , 1995, IEEE Trans. Syst. Man Cybern..

[29]  George J. Klir,et al.  Measures of uncertainty in the Dempster-Shafer theory of evidence , 1994 .

[30]  Ronald R. Yager,et al.  On the aggregation of prioritized belief structures , 1996, IEEE Trans. Syst. Man Cybern. Part A.

[31]  David Harmanec.  A NOTE ON UNCERTAINTY, DEMPSTER RULE OF COMBINATION, AND CONFLICT , 1997 .

[32]  R. Hartley.  Transmission of information , 1928 .

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

[34]  Claude E. Shannon,et al.  The Mathematical Theory of Communication , 1950 .

[35]  Isabelle Bloch,et al.  A first step toward automatic interpretation of SAR images using evidential fusion of several structure detectors , 1999, IEEE Trans. Geosci. Remote. Sens..

[36]  Weiru Liu,et al.  Reinvestigating Dempster's Idea on Evidence Combination , 2000, Knowledge and Information Systems.

[37]  P. Walley.  Measures of Uncertainty in Expert Systems , 1996, Artificial Intelligence.

[38]  Siegfried Gottwald,et al.  Fuzzy Sets and Fuzzy Logic , 1993 .

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

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

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

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

[43]  Isabelle Bloch,et al.  Application of Dempster-Shafer evidence theory to unsupervised classification in multisource remote sensing , 1997, IEEE Trans. Geosci. Remote. Sens..

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

[45]  D. Bell,et al.  Evidence Theory and Its Applications , 1991 .

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

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

[48]  Glenn Shafer,et al.  The combination of evidence , 1986, Int. J. Intell. Syst..

[49]  D. Dubois,et al.  A NOTE ON MEASURES OF SPECIFICITY FOR FUZZY SETS , 1985 .

[50]  George J. Klir,et al.  On the uniqueness of possibilistic measure of uncertainty and information , 1987 .

[51]  Babak Nadjar Araabi,et al.  Generalization of the Dempster-Shafer theory: a fuzzy-valued measure , 1999, IEEE Trans. Fuzzy Syst..

[52]  Ronald R. Yager,et al.  Arithmetic and Other Operations on Dempster-Shafer Structures , 1986, Int. J. Man Mach. Stud..

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

[54]  Frank Klawonn,et al.  On the axiomatic justification of Dempster's rule of combination , 1992, Int. J. Intell. Syst..

[55]  Azriel Rosenfeld,et al.  Evidence-based pattern-matching relaxation , 1993, Pattern Recognit..

[56]  Edward A. Bender,et al.  Mathematical methods in artificial intelligence , 1996 .

[57]  Jeffrey A. Barnett,et al.  Calculating Dempster-Shafer Plausibility , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[58]  Lotfi A. Zadeh,et al.  A Simple View of the Dempster-Shafer Theory of Evidence and Its Implication for the Rule of Combination , 1985, AI Mag..

[59]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

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

[61]  Hong Xu,et al.  Transferable belief model for decision making in the valuation-based systems , 1996, IEEE Trans. Syst. Man Cybern. Part A.

[62]  Hong Xu,et al.  Some strategies for explanations in evidential reasoning , 1996, IEEE Trans. Syst. Man Cybern. Part A.

[63]  Henri Prade,et al.  Representation and combination of uncertainty with belief functions and possibility measures , 1988, Comput. Intell..

[64]  Alfréd Rényi,et al.  Probability Theory , 1970 .

[65]  N. P. Mukherjee,et al.  On the Representation of Uncertain Information by Multidimensional Arrays , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[66]  Hakil Kim,et al.  Evidential reasoning approach to multisource-data classification in remote sensing , 1995, IEEE Trans. Syst. Man Cybern..