Download A Mathematical Theory of Hints: An Approach to the by Prof. Dr. Jürg Kohlas, Dr. Paul-André Monney (auth.) PDF

By Prof. Dr. Jürg Kohlas, Dr. Paul-André Monney (auth.)

The topic of the e-book is an method of the modeling of and the reasoning below uncertainty. It develops the Dempster-Shafer idea as a thought of the reliability of reasoning with doubtful arguments. a selected curiosity of this method is that it yields a brand new synthesis and integration of good judgment and chance concept. The reader will make the most of a brand new view at uncertainty modeling which extends classical chance theory.

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Additional resources for A Mathematical Theory of Hints: An Approach to the Dempster-Shafer Theory of Evidence

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A) of tin view of the measurements Xl and X2. b) of t in view of the measurement x. g. Dubois, Prade, 1985). 1. 7 Conc! usÎon 31 1. 7 Conclusion The examples of this chapter were selected to illustrate a uniform aud new approach to the treatment of a variety of different problems. The essence of the method is to model uncertainty by uncertain arguments with known probabilities or probability distributions and known consequences. In order to analyze certain hypotheses, proofs for these hypotheses or their negations are constructed using the available arguments.

3). The notion of hint must be extended in order that any infinite order Choquct capacity is the support function of some hint. This general theory will be presented in Part II of the book. Note that Shafer (1979) defines belief functions as Choquet capacities of infinite order without a reference to the notion of a hint. 6. If H is any subsei of e, then (1) pl(H) = max {pl(I) : I finite, I <;:: H} (2) sp(H) = min {sp(C): C cofinite,C"2 H}. The plausibility of any hypothesis is fully determined by the plausibilities of its finite subsets.

This shows how the credibility and plausibility of hypotheses can be evaluated in the light of the available evidence. These degrees measure the force with which the evidence supports or proves a hypothesis as well as the force with which the evidence disagrees with the hypothesis. ) with some error E. To simplify, we assume, to start with, that both T and the error take integer values. Furthermore, we suppose that the probability distribution of the error is known to be p( i) = P( E = i) for each relative integer i.

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