Geoscience Reference
In-Depth Information
where
(3.46)
By convention, r X ( x n +1 )=0, i.e. %=0. Hence substituting %=0 in Equation (3.45), the
total uncertainty in possibility theory is given by
(3.47)
Formula for transformation
For the transformation form probability to possibility or vice versa, ProUPosU, the
principle of uncertainty invariance requires that
H(p) = N(r) + S(r) = U T (r)
(3.48)
And the transformations are given by
Probability to possibility transformation (ProUPosU):
(3.49)
Possibility to probability transformation (PosUProU)
(3.50)
For simplicity x 1 ,…, x n are ordered such that p X (x i ) ! p X ( x i+ 1 ) and r X (x i ) ! r X ( x i+ 1 ) for all
i =1,…, n !1. For both way transformations (Eqs. (3.49) and (3.50)), the value of &
(0< & <1) is determined from the equality of the Equation (3.48). The transformation
procedure is also illustrated in Figure 3.5.
Search WWH ::




Custom Search