A Consistency-Specificity Trade-Off to Select Source Behavior in Information Fusion

Combining pieces of information provided by several sources without or with little prior knowledge about the behavior of the sources is an old yet still important and rather open problem in the belief function theory. In this paper, we propose an approach to select the behavior of sources based on a very general and expressive fusion scheme, that has the important advantage of making clear the assumptions made about the sources. The selection process itself relies on two cornerstones that are the notions of specificity and consistency of a knowledge representation, and that we adapt to the considered fusion scheme. We illustrate our proposal on different examples and show that the proposed approach actually encompasses some important existing fusion strategies.

[1]  Philippe Smets,et al.  Analyzing the combination of conflicting belief functions , 2007, Inf. Fusion.

[2]  Luc Jaulin,et al.  Robust set-membership state estimation; application to underwater robotics , 2009, Autom..

[3]  Nic Wilson.  Algorithms for Dempster-Shafer Theory , 2000 .

[4]  Eric LEFEVRE,et al.  ABOUT THE USE OF DEMPSTER SHAFER THEORY FOR COLOR IMAGE SEGMENTATION , 2002 .

[5]  Eric Lefevre,et al.  Knowledge modeling methods in the framework of evidence theory: an experimental comparison for melanoma detection , 2000, Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics. 'cybernetics evolving to systems, humans, organizations, and their complex interactions' (cat. no.0.

[6]  Weiru Liu,et al.  Bridging Jeffrey's Rule, AGM Revision and Dempster Conditioning in the Theory of Evidence , 2011, Int. J. Artif. Intell. Tools.

[7]  Johan Schubert,et al.  Conflict management in Dempster-Shafer theory using the degree of falsity , 2011, Int. J. Approx. Reason..

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

[9]  Alessandro Saffiotti,et al.  The Transferable Belief Model , 1991, ECSQARU.

[10]  Sébastien Destercke,et al.  Evaluating Data Reliability: An Evidential Answer with Application to a Web-Enabled Data Warehouse , 2013, IEEE Transactions on Knowledge and Data Engineering.

[11]  Thierry Denoeux,et al.  Relevance and truthfulness in information correction and fusion , 2012, Int. J. Approx. Reason..

[12]  Christophe Osswald,et al.  Contradiction measures and specificity degrees of basic belief assignments , 2011, 14th International Conference on Information Fusion.

[13]  Thierry Denoeux,et al.  Inner and Outer Approximation of Belief Structures Using a Hierarchical Clustering Approach , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Thierry Denoeux.  A k -Nearest Neighbor Classification Rule Based on Dempster-Shafer Theory , 2008, Classic Works of the Dempster-Shafer Theory of Belief Functions.

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

[16]  Olivier Colot,et al.  Automatic discounting rate computation using a dissent criterion , 2010 .

[17]  Frédéric Pichon.  On the α-Conjunctions for Combining Belief Functions , 2012, Belief Functions.

[18]  Zied Elouedi,et al.  Discountings of a Belief Function Using a Confusion Matrix , 2010, 2010 22nd IEEE International Conference on Tools with Artificial Intelligence.

[19]  F. Pichon.  Interpretation and Computation of α-Junctions for Combining Belief Functions , 2009 .

[20]  Weiru Liu,et al.  Analyzing the degree of conflict among belief functions , 2006, Artif. Intell..

[21]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[22]  Christophe Labreuche,et al.  Multidimensional Approach to Reliability Evaluation of Information Sources , 2014 .

[23]  Serafín Moral,et al.  Difference of entropies as a non-specificity function on credal sets† , 2005, Int. J. Gen. Syst..

[24]  Frédéric Pichon,et al.  Fonctions de croyance : décompositions canoniques et règles de combinaison. (Belief functions: canonical decompositions and combination rules) , 2009 .

[25]  Quan Pan,et al.  Combination of sources of evidence with different discounting factors based on a new dissimilarity measure , 2011, Decis. Support Syst..

[26]  Thierry Denoeux,et al.  Refined modeling of sensor reliability in the belief function framework using contextual discounting , 2008, Inf. Fusion.

[27]  Francesc Reventos,et al.  Uncertainty and sensitivity analysis of the LOFT L2-5 test: Results of the BEMUSE programme , 2008 .

[28]  Didier Dubois,et al.  Idempotent conjunctive combination of belief functions: Extending the minimum rule of possibility theory , 2011, Inf. Sci..

[29]  Alex M. Andrew,et al.  Uncertainty and Information: Foundations of Generalized Information Theory , 2006 .

[30]  Thomas Burger,et al.  Toward an Axiomatic Definition of Conflict Between Belief Functions , 2013, IEEE Transactions on Cybernetics.

[31]  J. Dezert,et al.  Information fusion based on new proportional conflict redistribution rules , 2005, 2005 7th International Conference on Information Fusion.

[32]  T. Denoeux,et al.  Interpretation and Computation of alpha-Junctions for Combining Belief Functions , 2009 .

[33]  Anne-Laure Jousselme,et al.  Distances in evidence theory: Comprehensive survey and generalizations , 2012, Int. J. Approx. Reason..

[34]  Dong-Ling Xu,et al.  Evidential reasoning rule for evidence combination , 2013, Artif. Intell..

[35]  Thomas Burger,et al.  Selecting Source Behavior in Information Fusion on the Basis of Consistency and Specificity , 2013, ECSQARU.

[36]  John Grant,et al.  Measuring Consistency Gain and Information Loss in Stepwise Inconsistency Resolution , 2011, ECSQARU.

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

[38]  Joaquín Abellán,et al.  Measures of divergence on credal sets , 2006, Fuzzy Sets Syst..

[39]  Christophe Osswald,et al.  Conflict measure for the discounting operation on belief functions , 2008, 2008 11th International Conference on Information Fusion.

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

[41]  Chongzhao Han,et al.  Discounted combination of unreliable evidence using degree of disagreement , 2013, Int. J. Approx. Reason..

[42]  Sébastien Destercke,et al.  Methods for the evaluation and synthesis of multiple sources of information applied to nuclear computer codes , 2008 .

[43]  John Grant,et al.  Measuring the Good and the Bad in Inconsistent Information , 2011, IJCAI.

[44]  Ph. Smets,et al.  THE CONCEPT OF DISTINCT EVIDENCE , 1999 .

[45]  Didier Dubois,et al.  A definition of subjective possibility , 2008, Int. J. Approx. Reason..

[46]  D. Dubois,et al.  A set-theoretic view of belief functions: Logical operations and approximations by fuzzy sets , 1986 .