Download A Methodology for Uncertainty in Knowledge-Based Systems by Kurt Weichselberger PDF

By Kurt Weichselberger

In this e-book the resultant use of likelihood idea is proposed for dealing with uncertainty in professional platforms. it really is proven that equipment violating this advice can have risky results (e.g., the Dempster-Shafer rule and the tactic utilized in MYCIN). the need of a few requisites for an accurate combining of doubtful details in specialist platforms is established and compatible principles are supplied. the prospect is considered that period estimates are given rather than designated information regarding possibilities. For combining details containing period estimates ideas are supplied that are important in lots of cases.

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12b) These formulas can already be found in STRASSEN [1964], who refers to a result of CHOQUET [1953/54] according to which P , is a totally monotone capacity respectively P* a totally alternating capacity. The definition of a n-monotone respectively n-alternating set function F is the following: F(B) _>E F(B N Bi) - P, F(B N Bi N Bi) + - . . 13a) F(B) < F~F(B U Bi) - ~ F(B U Bi U Bj) + - . . UBn) i i

S u m m i n g up we obtain: k k k k k Bel (-~Ei) = k E U I = k'jE1L j EILi + i=El(¢~ + ¢iE3 + . . i=1 "= "= "= k k k k i__EIUi+ iEiLi = k - (k - 2) i__EILi-i_El(¢iE2+ . . +¢Eik-i) +7~ik-1) As the n u m b e r of the (EjIU ... -r,k_~ k For ~k = re(B) >_ 0 it is: k k E (Ui+Li) > k - (k-2) [iE1Li + ~a + Na + - . + ~k = 1 i=! [] Concerning the sufficiency of this condition we shall formulate a weaker statement. 20) holds. 20) and feasibility) [] 43 We shall not discuss the sufficient conditions for D-S-admissibility in the case of k > 4 because these conditions are rather complicated and do not provide a new insight into this problem.

335]. Dempster's explanation makes it clear that there is an important difference between the present approach and the various decision-theoretic methods to combine subjective probability distributions, methods which inevitably accept the presupposition that all probability distributions are influenced by some common information. Obviously classical probability theory does not provide immediate solutions for the problem Dempster has in mind. ,Ek- If the additional information is given, that a certain experiment produced the same result for each of the 1 variables, then the probability that this outcome is El*, is given by Pl(Ei*) " .

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