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

By Kurt Weichselberger

In this booklet the resultant use of likelihood conception is proposed for dealing with uncertainty in professional platforms. it's proven that tools violating this advice can have risky effects (e.g., the Dempster-Shafer rule and the tactic utilized in MYCIN). the need of a few specifications for an accurate combining of doubtful info in professional platforms is verified and compatible ideas are supplied. the chance is considered that period estimates are given rather than targeted information regarding percentages. For combining details containing period estimates ideas are supplied that are priceless in lots of cases.

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Only for c) does the sum of all lower and upper limits exceed the value 2. 6 m(EiUEj) = 0 . 2 The same calculation could be carried out for the estimates b) and d). 18) and with the interpretation of Li as belief functions and Ui as upper probabilities. [] Through this definition the requirements of Shafer's theory of belief functions, concerning the concept of k - P R I s - which in itself is not a topic of Shafer's - are characterized. 2): Be 0 = {El . . , Ek} k j~ILj - Li+~ti~2+;~i3' + "'" +;ti~n-I Be] (TEl) = 1 - U i = where k j I-I E2 = Y, Y~ m(EJl U EJ2) Jl =2 J2 =1 k Ji-1 jl ~" j2;~" and N1 analogously corresponds to the 1-times s u m m a t i o n of m(Ejl U .

2 0 ; P(E4) = U4 = 0 . 5 2 ~ P(E1) = L, = 0 . 0 0 ; P(E3) = U s = 0 . 3 0 ; P(Ea) = 0 . 2 8 : s4 ; P(E~) = U4 = 0 . 18 : t P(E2) = 0 . 2 8 : s5 P(E4) = L4= 0 . 22 : s6 P(E3) = L3 = 0 . 2 0 ; P(E4) = L4 = 0 . 4 8 ~ P(E2) = 0 . 2 2 : sr P(E1) = UI = 0 . 1 0 ; P(E3) = U3 = 0 . 3 0 ; P(E4) = L4 = 0 . 4 8 ~ P(E2) = 0 . 1 2 : ss P(E1) = U1 = 0 . 1 0 ; P(E3) = L 3 = 0 . 2 0 ; P(E4) = U4 = 0 . 5 2 ~ P(E2) = 0 . 1 8 : s9 P(E,) = L1 = 0 . 0 0 ; P(E3) =U3 = 0 . 3 0 ; P(E4) = U4= 0 . 18 P(E2) = L 2 = 0 . 1 0 ; P(E4) = U 4 = O .

D) ~Ui>l- 11 Then: ~ L i and ~ U i > l "MI I2 ZLi "~I2 P*(B1) + P*(B2) = 1 - Z Li + 1 - Z Li = -ql -~I2 =2 - Z Li - Z Li >_pa(B1 U B2) + P*(B1 N B2) (-~II)U (~12) ("ql) f] ("112) because of inequality 4). 5a) holds in each of the four cases. 58 > P,(BI) + P,(B2) = = 0 . 1 8 + 0 . 5a) is sufficient to produce a feasible k - P R I , is not of the same importance for our considerations as the question of necessity. 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].

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