Toward a combination rule to deal with partial conflict and specificity in belief functions theory

We present and discuss a mixed conjunctive and disjunctive rule, a generalization of conflict repartition rules, and a combination of these two rules. In the belief functions theory one of the major problem is the conflict repartition enlightened by the famous Zadeh's example. To date, many combination rules have been proposed in order to solve a solution to this problem. Moreover, it can be important to consider the specificity of the responses of the experts. Since few year some unification rules are proposed. We have shown in our previous works the interest of the proportional conflict redistribution rule. We propose here a mixed combination rule following the proportional conflict redistribution rule modified by a discounting procedure. This rule generalizes many combination rules.

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

[2]  Alain Appriou.  Approche générique de la gestion de l'incertain dans les processus de fusion multisenseur Generic approach of the uncertainty management in multisensor fusion processes , 2005 .

[3]  Jean Dezert,et al.  Applications and Advances of DSmT for Information Fusion , 2004 .

[4]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[5]  Christophe Osswald,et al.  Understanding the large family of Dempster-Shafer theory's fusion operators - a decision-based measure , 2006, 2006 9th International Conference on Information Fusion.

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

[7]  Éloi Bossé,et al.  A new distance between two bodies of evidence , 2001, Inf. Fusion.

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

[9]  Pierre Valin,et al.  Adaptative combination rule and proportional conflict redistribution rule for information fusion , 2006, ArXiv.

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

[11]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

[12]  P. Vannoorenberghe,et al.  Strategies for combining conflicting dogmatic beliefs , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

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

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

[15]  Adam Krzyżak,et al.  Methods of combining multiple classifiers and their applications to handwriting recognition , 1992, IEEE Trans. Syst. Man Cybern..

[16]  Christophe Osswald,et al.  A new generalization of the proportional conflict redistribution rule stable in terms of decision , 2008, ArXiv.

[17]  Ching Y. Suen,et al.  Application of majority voting to pattern recognition: an analysis of its behavior and performance , 1997, IEEE Trans. Syst. Man Cybern. Part A.

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

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

[20]  Jean Dezert,et al.  Proportional Conflict Redistribution Rule , 2004, ArXiv.

[21]  Toshiyuki Inagaki.  Interdependence between safety-control policy and multiple-sensor schemes via Dempster-Shafer theory , 1991 .

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

[23]  A. Appriou.  01 - Approche générique de la gestion de l’incertain dans les processus de fusion multisenseur , 2005 .

[24]  Eric Lefevre,et al.  Belief function combination and conflict management , 2002, Inf. Fusion.

[25]  Arie Tzvieli.  Possibility theory: An approach to computerized processing of uncertainty , 1990, J. Am. Soc. Inf. Sci..

[26]  Thierry Denoeux.  The cautious rule of combination for belief functions and some extensions , 2006, 2006 9th International Conference on Information Fusion.

[27]  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.