Belief function to probability: A tradeoff between easy decision-making and high risk

The problem of probability transformation is crucial for decision-making in Dempster-Shafer Theory of evidence. In this paper, a compromise method has been proposed for transforming basic probability assignment to probability function. The novel transformation method can acquire better balance between easy decision-making and high risk. Numerical examples are used to illustrate the rationality and efficiency of the proposed method.

[1]  J. J. Sudano.  The system probability information content (PIC) relationship to contributing components, combining independent multi-source beliefs, hybrid and pedigree pignistic probabilities , 2002, Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997).

[2]  Don H. Johnson,et al.  Symmetrizing the Kullback-Leibler Distance , 2001 .

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

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

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

[6]  Chongzhao Han,et al.  Is entropy enough to evaluate the probability transformation approach of belief function? , 2010, 2010 13th International Conference on Information Fusion.

[7]  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.

[8]  Jean Dezert,et al.  A new probabilistic transformation of belief mass assignment , 2008, 2008 11th International Conference on Information Fusion.

[9]  XU Xiao-bin,et al.  A New Similarity Measure Between Generalized Trapezoidal Fuzzy Numbers and Its Application to Fault Diagnosis , 2011 .

[10]  Quan Pan,et al.  A new belief-based K-nearest neighbor classification method , 2013, Pattern Recognit..

[11]  Fabio Cuzzolin.  The Intersection Probability and Its Properties , 2009, ECSQARU.

[12]  Deqiang Han,et al.  Hierarchical DSmP transformation for decision-making under uncertainty , 2012, 2012 15th International Conference on Information Fusion.

[13]  Lockheed Martin,et al.  Yet Another Paradigm Illustrating Evidence Fusion (YAPIEF) , 2006, 2006 9th International Conference on Information Fusion.

[14]  J. J. Sudano.  Equivalence between belief theories and naive bayesian fusion for systems with independent evidential data: part II, the example , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

[15]  John J. Sudano.  Pignistic Probability Transforms for Mixes of Low- and High-Probability Events , 2015, ArXiv.

[16]  Fabio Cuzzolin.  On the Properties of the Intersection Probability , 2007 .

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

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

[19]  Huaiyu Zhu.  On Information and Sufficiency , 1997 .

[20]  Zhe Zhou,et al.  An Optimal Method for Combining Conflicting Evidences , 2012 .

[21]  J.J. Sudano.  Equivalence between belief theories and naive bayesian fusion for systems with independent evidential data: part I, the theory , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.