Combination calculi for uncertainty reasoning: representing uncertainty using distributions |
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Authors: | Robert Hummel Larry M Manevitz |
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Affiliation: | (1) Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA;(2) Department of Mathematics and Computer Science, University of Haifa, Haifa, 31905, Israel |
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Abstract: | There are many different methods for incorporating notions of uncertainty in evidential reasoning. A common component to these
methods is the use of additional values, other than conditional probabilities, to assert current degrees of belief and certainties
in propositions. Beginning with the viewpoint that these values can be associated with statistics of multiple opinions in
an evidential reasoning system, we categorize the choices that are available in updating and tracking these multiple opinions.
In this way, we develop a matrix of different uncertainty calculi, some of which are standard, and others are new. The main
contribution is to formalize a framework under which different methods for reasoning with uncertainty can be evaluated. As
examples, we see that both the “Kalman filtering” approach and the “Dempster–Shafer” approach to reasoning with uncertainty
can be interpreted within this framework of representing uncertainty by the statistics of multiple opinions.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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