On the fusion of imprecise uncertainty measures using belief structures

Our interest is in the fusion of information from multiple sources when the information provided by the individual sources is expressed in terms of an imprecise uncertainty measure. We observe that the Dempster-Shafer belief structure provides a framework for the representation of a wide class of imprecise uncertainty measures. We then discuss the fusion of multiple Dempster-Shafer belief structures using the Dempster rule and note the problems that can arise when using this fusion method because of the required normalization in the face of conflicting focal elements. We then suggest some alternative approaches fusing multiple belief structures that avoid the need for normalization.

[1]  G. Choquet Theory of capacities , 1954 .

[2]  Ronald R. Yager,et al.  On the retranslation process in Zadeh's paradigm of computing with words , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  Inés Couso,et al.  Approximations of upper and lower probabilities by measurable selections , 2010, Inf. Sci..

[4]  Didier Dubois,et al.  Decision-making Process , 2009 .

[5]  Edward Beltrami,et al.  Uncertainty and Information , 2020, What Is Random?.

[6]  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.

[7]  Arthur P. Dempster,et al.  New Methods for Reasoning Towards PosteriorDistributions Based on Sample Data , 1966, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[8]  Shanlin Yang,et al.  Analyzing the applicability of Dempster's rule to the combination of interval-valued belief structures , 2011, Expert Syst. Appl..

[9]  James Llinas,et al.  An introduction to multisensor data fusion , 1997, Proc. IEEE.

[10]  Javier Montero,et al.  Modelling uncertainty , 2010, Inf. Sci..

[11]  Okyay Kaynak,et al.  Computational Intelligence: Soft Computing and Fuzzy-Neuro Integration with Applications , 1998, NATO ASI Series.

[12]  Makoto Itoh,et al.  Theory of Evidence , 1998 .

[13]  Montserrat Casanovas Ramón,et al.  Decision making wih demspter-shafer theory and uncertain induced aggregation operators , 2008 .

[14]  Arthur P. Dempster,et al.  A Generalization of Bayesian Inference , 1968, Classic Works of the Dempster-Shafer Theory of Belief Functions.

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

[16]  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..

[17]  Koichi Yamada,et al.  A new combination of evidence based on compromise , 2008, Fuzzy Sets Syst..

[18]  H. B. Mitchell,et al.  Multi-Sensor Data Fusion: An Introduction , 2007 .

[19]  Ronald R. Yager,et al.  Essentials of fuzzy modeling and control , 1994 .

[20]  Juan Carlos Augusto,et al.  Mass function derivation and combination in multivariate data spaces , 2010, Inf. Sci..

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

[22]  Lotfi A. Zadeh,et al.  Is there a need for fuzzy logic? , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

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

[24]  Tzu-Chao Lin,et al.  Switching-based filter based on Dempster's combination rule for image processing , 2010, Inf. Sci..

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

[26]  George J. Klir,et al.  On the problem of retranslation in computing with perceptions , 2006, Int. J. Gen. Syst..

[27]  Witold Pedrycz,et al.  Fuzzy Systems Engineering - Toward Human-Centric Computing , 2007 .

[28]  Ronald R. Yager,et al.  Entropy and Specificity in a Mathematical Theory of Evidence , 2008, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[29]  Ronald R. Yager,et al.  Classic Works of the Dempster-Shafer Theory of Belief Functions , 2010, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[30]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU)--an outline , 2005, Inf. Sci..

[31]  C. Wagner,et al.  Rational Consensus in Science and Society , 1981 .

[32]  Jian-Bo Yang,et al.  On the combination and normalization of interval-valued belief structures , 2007, Information Sciences.