Journal Article10.1109/21.328933
Conditional events, conditioning, and random sets
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TL;DR: A new approach to a solution of the Dempster/Shafer theory of evidence problem by establishing a link between conditional events and discrete random sets and an updating rule is introduced that is equivalent to the law of total probability if all beliefs are probabilities.
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Abstract: A central problem in the Dempster/Shafer theory of evidence is conditioning. This paper presents a new approach to a solution of this problem by establishing a link between conditional events and discrete random sets. Conditional events are introduced as sets of equivalent events under conditioning. These sets may become targets of a multivalued mapping. Thus, conditional belief functions can be introduced. Both Bayesian and pure random set conditioning rules are derived and discussed. Random set conditioning allows expressing conditional degrees of belief when marginal beliefs are unknown. Finally, an updating rule is introduced that is equivalent to the law of total probability (Jeffrey's rule) if all beliefs are probabilities. >
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Citations
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Ronald R. Yager,Janusz Kacprzyk,Mario Fedrizzi +2 more
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TL;DR: The Dempster-Shafer Theory of Evidence is applied as a guide for the management of uncertainty in knowledge-based systems.
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Linear utility theory for belief functions
TL;DR: In uncertainty situations where knowledge is described by a Dempster-Shafer belief function (which is more general than a probability measure), von Neumann-Morgenstern linear utility theory applies and leads to a generalized expected utility representation of preference as discussed by the authors.
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Propagating belief functions in qualitative Markov trees
TL;DR: It is shown that efficient implementation of Dempster's rule is possible if the questions or partitions for which the authors have evidence are arranged in a qualitative Markov tree—a tree in which separations indicate relations of qualitative conditional independence.
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A valuation-based language for expert systems
TL;DR: A new language based on valuations is proposed as an alternative to rule-based languages for constructing knowledge-based systems and the ability of such a language to maintain consistency and cache inferences is demonstrated with an example.
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