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

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

ISBN-10: 3540591761

ISBN-13: 9783540591764

ISBN-10: 3662016745

ISBN-13: 9783662016749

The topic of the publication is an method of the modeling of and the reasoning lower than uncertainty. It develops the Dempster-Shafer thought as a concept of the reliability of reasoning with doubtful arguments. a selected curiosity of this strategy is that it yields a brand new synthesis and integration of common sense and likelihood idea. The reader will take advantage of a brand new view at uncertainty modeling which extends classical chance theory.

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

Example text

In order to avoid contradictions, for each defective device i, there must be a failure mode wj(i) such that Xi - tE r(wj(i)). Hence we have e. cred(t) =k L {et ID1 (1- et)IFI. 14) iED D+F= {1, ... ,n},F;l0}. The case F = 0 were al! devices are defective is excluded in the sum, because we make the further assumption, that in this case there is no way to prove t. This excludes in particular the case where a defective device has a known error distribution. But even in this and similar cases, we may assume - in an appraximate analysis - that the probability of alI devices failing is negligible.

This is a hint of statistical nature. Suppose that the night you travel is in autumn. If you are unlucky enough for your Monday to falI on a strike day (possibility wd, then r(wd = {s}. Otherwise, if you assume that your Monday is not a strike day (possibility wz), then r(wz) = {-,s}. The probabilities of the two possibilities are estimated by the statistical information as x /30 and (30 x) /30 respectively. Then, of course, the question arises as to how to combine these two hints to get an overall appreciation of your risk regarding the strike.

If it dates from this Sunday (interpretation wd, then surely you must be prepared to take a taxi, r(wd = {s}. lf, however, you assume that the newspaper is an old one (interpretation wz), then nothing can be said about the question of a strike because you may stil! be confronted with a strike and thus r(wz) = The probabilities you assign to the two possible interpretations depend on the appearance of the piece of newspaper. If it is clean and fresh, then you may give a larger probability to Wj than if it is crumpled and dirty.

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

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