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 publication is an method of the modeling of and the reasoning below uncertainty. It develops the Dempster-Shafer thought as a idea 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 good judgment and likelihood idea. The reader will reap the benefits of a brand new view at uncertainty modeling which extends classical likelihood 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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The following theorem states a very basic property of support functions and plausibility functions. 5. e. L {( _1)1 / 1+ Sp(niEIHi ) : 01= 1 ~ {I, ... 8) for all n 2: 1 and all subsets H, Hi of 8 such that H ;2 Hi for ali i = 1, ... ,n. e. pl(H) :::; L {( -l)III+Ipl(UiEIHi) : 01= 1 ~ {1, ... 3Uch that H ~ Hj for ali i = 1, ... ,n. 2 Elementary Properties of Support and Plausibility Functions 43 This theorem was proved by Shafer (1976 a) for finite frames of discernment e, but it extends easily also to infinite frames.

So, to each hint 1{ = (n, P, r, 8) corresponds exactly one support function and one credibility function, both defined an P( 8). Let's collect a few important basic results about support and plausibility functions. 4. (1) If HI ;2 Hz ;2 ... 5) Sp(Hi)' ' .... 00 (2) lf HI ~ Hz ;2 ... 7) ,Iim pl(Hi). ' .... 00 This theorem asserts that the set functions sp and pl are continuous. The following theorem states a very basic property of support functions and plausibility functions. 5. e. L {( _1)1 / 1+ Sp(niEIHi ) : 01= 1 ~ {I, ...

At any time of the discourse a fixed wiU be considered, which is called the (actual) frame of discernmeni. It becomes thus necessary to consider dynamically changing frames of discernment. This wiU be discussed in Chap. 6, whereas for the moment ewill be considered as a fixed set. e e It may also become necessary or useful to consider statements which are cruder than single answers. For example, one might be interested in the statement "the temperature will be below zero degree centigrade" or "the murderer was left-handed".

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