Constructing Belief Functions from Qualitative Expert Opinions

A new method for constructing belief functions from elicited expert opinions is proposed. It consists in representing qualitatively expert opinions in terms of preference relations. These relations are transformed into constraints of an optimization problem whose resolution allows the generation of the least informative belief functions according to some uncertainty measures. Mono-objective and multiobjective optimization techniques are used to optimize, respectively, one or simultaneously different uncertainty measures

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

[2]  S. K. Michael Wong,et al.  Representation of Qualitative User Preference by Quantitative Belief Functions , 1994, IEEE Trans. Knowl. Data Eng..

[3]  Yiyu Yao,et al.  Axiomatization of qualitative belief structure , 1991, IEEE Trans. Syst. Man Cybern..

[4]  G. Klir,et al.  Uncertainty-based information: Elements of generalized information theory (studies in fuzziness and soft computing). , 1998 .

[5]  James C. Bezdek,et al.  Uncertainty measures for evidential reasoning II: A new measure of total uncertainty , 1993, Int. J. Approx. Reason..

[6]  James C. Bezdek,et al.  Uncertainty measures for evidential reasoning I: A review , 1992, Int. J. Approx. Reason..

[7]  Bernard Roy,et al.  Preferences and numbers , 2001 .

[8]  Fouad Ben Abdelaziz,et al.  Decision-maker's preferences modeling in the stochastic goal programming , 2005, Eur. J. Oper. Res..

[9]  Simon Parsons,et al.  Some qualitative approaches to applying the Dempster-Shafer theory , 1994 .

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

[11]  Kweku-Muata Osei-Bryson,et al.  A process for generating quantitative belief functions , 1999, Eur. J. Oper. Res..

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

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

[14]  Bilal M. Ayyub,et al.  Elicitation of expert opinions for uncertainty and risks: Answer to the Book Review by Roger M. Cooke , 2003, Fuzzy Sets Syst..