Using Logic to Understand Relations between DSmT and Dempster-Shafer Theory

In this paper, we study the relations that exist between Dempster-Shafer Theory and one of its extensions named DSmT. In particular we show, by using propositional logic, that DSmT can be reformulated in the classical framework of Dempster-Shafer theory and that any combination rule defined in the DSmT framework corresponds to a rule in the classical framework. The interest of DSmT rather concerns the compacity of expression it manipulates.

[1]  Rudolf Kruse,et al.  Qualitative and Quantitative Practical Reasoning , 1997, Lecture Notes in Computer Science.

[2]  Jürg Kohlas,et al.  Representation of Evidence by Hints , 2008, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[3]  Jérôme Lang,et al.  Logical Preference Representation and Combinatorial Vote , 2004, Annals of Mathematics and Artificial Intelligence.

[4]  Alain Appriou,et al.  Multisensor Data Fusion in Situation Assessment Processes , 1997, ECSQARU-FAPR.

[5]  Jean Dezert,et al.  Foundations for a new theory of plausible and paradoxical reasoning , 2002 .

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

[7]  Jean Dezert,et al.  An Introduction to the DSm Theory for the Combination of Paradoxical, Uncertain, and Imprecise Sources of Information , 2006, ArXiv.

[8]  M. Sarfraz.  Computer-Aided Intelligent Recognition Techniques and Applications , 2005 .

[9]  Philippe Smets.  Probability of Provability and Belief Functions , 1999 .

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

[11]  Isabelle Bloch,et al.  Improving Mine Recognition through Processing and Dempster–Shafer Fusion of Multisensor Data , 2005 .

[12]  Philippe Smets,et al.  Classification Using Belief Functions: Relationship Between Case-Based and Model-Based Approaches , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[14]  L. Cholvy.  Applying theory of evidence in multisensor data fusion: a logical interpretation , 2000, Proceedings of the Third International Conference on Information Fusion.

[15]  Milan Daniel.  A Generalization of the Classic Combination Rules to DSm Hyper-power Sets , 2006 .

[16]  Milan Daniel.  Contribution of DSm Approach to the Belief Function Theory , 2008 .

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

[18]  Laurence Cholvy.  Data Merging: Theory of Evidence vs. Knowledge-Bases Merging Operators , 2001, ECSQARU.

[19]  Thierry Denoeux,et al.  Decision fusion for postal address recognition using belief functions , 2009, Expert Syst. Appl..