By Kurt Weichselberger
In this ebook the resultant use of chance concept is proposed for dealing with uncertainty in specialist structures. it's proven that equipment violating this recommendation could have harmful results (e.g., the Dempster-Shafer rule and the strategy utilized in MYCIN). the need of a few standards for an accurate combining of doubtful details in professional structures is established and appropriate principles are supplied. the prospect is considered that period estimates are given rather than particular information regarding chances. For combining details containing period estimates principles are supplied that are worthy in lots of cases.
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Extra info for A Methodology for Uncertainty in Knowledge-Based Systems
5a) in the case of a finite sample space produce upper and lower envelopes of a set of probability measures, which is equivalent to what we call a feasible k - P R I [HUBER and STRASSEN, 1973; HUBER, 1973]. Therefore we can state the following result: The set of feasible k-PRIs is identical to the set of 2-alternating (respectively 2-monotone) Choquet-capacities. While these results are mainly of theoretical interest as far as k - P R I s are concerned, they will be of great help when we come to characterize related concepts.
P(E,) = L , = 0 . 1 2 ; P(E2) =L2 = 0 . 1 5 P(E1) = L , = 0 . 1 2 ; P(Eu) =152 = 0 . 2 4 ; P(E3) = ; P(E3) =Us = 0 . 3 6 ~ L3 = 0 . 2 3 ~ P(E,) : U, = 0 . 1 7 ; r ( E 2 ) : L2 = 0 . 1 5 ; P ( E a ) = L 3 = 0 . 2 3 ~ P(E1) =UI = 0 . 1 7 P(E1) = U a = 0 . 1 7 ; P(E,) = L , = 0 . 1 2 P(E4) = 0 . 41 : s2 P(E4) = 0 . 4 5 : t ; P(e2) =U2 = 0 . 2 4 ; P(E3) = L3 = 0 . 2 3 ~ P(E4) = 0 . 3 6 : s3 P(E2) =L2 = 0 . 1 5 ; P(E3) =U3 = 0 . 3 6 ~ P(E4) = 0 . 3 2 : s4 ; P(E2) =U2 = 0 . 2 4 ; P(Es) =U3 = 0 . 3 6 ~ P(E4) = 0 .
1 2 : s5 P(E2) = U 2 = 0 . 2 4 ; = 0 . 1 2 : s2 P(E3) = L 3 = 0 . 2 3 ; P(E4) = U 4 = 0 . 4 1 ~ P ( E t ) P(E2) = L 2 = 0 . 1 5 ; P(E3) = U 3 = 0 . 3 6 ; P(E4) = U 4 = 0 . 08 : t So the two equations, each causing degeneracy, reduce the number of corners by two, but the same process reduces the number of failing candidates, which was 12 in the case of non-degeneracy, to eight.  We shall have a closer examination of the problems relating to the structure of a k - P R I for consideration in the framework of a more specialized study.