Aggregating Imprecise Probabilistic Knowledge

The problem of aggregating two or more sources of information containing knowledge about a same domain is considered. We propose an aggregation rule for the case where the available information is modeled by coherent lower previsions, corresponding to convex sets of probability mass functions. The consistency between aggregated beliefs and sources of information is discussed. A closed formula, which specializes our rule to a particular class of models, is also derived. Finally, an alternative ex planation of Zadeh’s paradox is provided.

[1]  Marco Zaffalon The naive credal classifier , 2002 .

[2]  Marco Zaffalon,et al.  Limits of Learning about a Categorical Latent Variable under Prior Near-Ignorance , 2007, Int. J. Approx. Reason..

[3]  Enrique Miranda Updating coherent previsions on finite spaces , 2009, Fuzzy Sets Syst..

[4]  Stefan Arnborg,et al.  Robust Bayesianism : Imprecise and Paradoxical Reasoning , 2004 .

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

[6]  Thomas Lukasiewicz,et al.  Reasoning with imprecise probabilities , 2000, Int. J. Approx. Reason..

[7]  P. Walley Statistical Reasoning with Imprecise Probabilities , 1990 .

[8]  Gert de Cooman,et al.  Epistemic irrelevance in credal nets: The case of imprecise Markov trees , 2010, Int. J. Approx. Reason..

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

[10]  R. Haenni Shedding new light on Zadeh's criticism of Dempster's rule of combination , 2005, 2005 7th International Conference on Information Fusion.

[11]  Yaakov Bar-Shalom,et al.  Multitarget-multisensor tracking: Advanced applications , 1989 .

[12]  Gert de Cooman,et al.  Extension of coherent lower previsions to unbounded random variables , 2002 .

[13]  Didier Dubois,et al.  Possibility theory , 2018, Scholarpedia.

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

[15]  Gert de Cooman,et al.  Coherent lower previsions in systems modelling: products and aggregation rules , 2004, Reliab. Eng. Syst. Saf..

[16]  P. Walley Measures of Uncertainty in Expert Systems , 1996, Artificial Intelligence.