By Kurt Weichselberger

In this booklet the resultant use of likelihood thought is proposed for dealing with uncertainty in specialist structures. it truly is proven that tools violating this advice could have risky outcomes (e.g., the Dempster-Shafer rule and the strategy utilized in MYCIN). the need of a few standards for an accurate combining of doubtful info in professional structures is verified and compatible ideas are supplied. the prospect is considered that period estimates are given rather than specific information regarding percentages. For combining info containing period estimates principles are supplied that are precious in lots of cases.

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32. [] The question, whether it is necessary to go through the listing of all corners of S* in order to achieve this result, is answered by the following theorem. ,k} and B = U El, then icI P,(B) : Max[ r. 5): Obviously the extreme values must be found in a corner of S*. In such a corner at least k-1 probabilities take either their maximal or their minimal value. For the calculation of P*(B) we distinguish three cases: 1) EVi+ E Li=l. 9) is valid in this case. 2) E U i + E Li>l. i~I i~I k Because of ~ Li < I it must be possible to find a corner for which i=I P(Ei) =Li for all i g I and E P(Ei) + E L i = l .

It is easy to construct examples for which these differences become much greater. 7). 5, both resulting from P1(EI') = 0 . 4 P2(EI') = 0 . 6667 Again the probability of E3 = E3' is estimated higher, if at first the combination takes place and afterwards the coarsening is done. 23). 08 m (0) = ml ( E l ' ) . m 2 ( E 3 ' ) + m l ( E 3 ' ) . m 2 ( E l ' ) + m l ( E l ' ) . 08 < P(E3') _<0 . 7 6 . 8) we obtain: m ( E l ' ) =m(E1) +m(E2) + m(E,UE2) = 0 . 2 4 re(E3') =re(E3) = 0 . 23) is applied afterwards.

Since this rule cannot be derived from laws of probability, it is legitimate to search for competing solutions for the considered problem and to compare the behaviour of such solutions. 21) to cases in which interval estimates of probabilities are used. e. a set of probability distributions. 21) leads to a value P(Ei*) for every selection of one distribution out of each structure. 21). 48 Let us for simplicity take 1 = 2. The two k - P R I s correspond to the structures S* and S~, so that Sup Pj(Ei) = Uji PieS~ I n f Pj(Ei) =Lji PjeS]' j=1,2 ; i = l .

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