EXISTING MATHEMATICAL METHODS FOR UNCERTAINTY ASSESSMENT - Modelling Uncertainty in Flood Forecasting Systems - page 41

various aspects of probability-possibility relationships. Klir and Wierman (1998)
presented good reviews of various transformation methods reported in the literature until
1997. Except from the normalisation requirements these methods substantially differ
from one another.
Most of the conversion methods from probability to possibility or vice versa use the
formula of the form:
(3.35)
where r X (x) and p X (x) are possibility and probability distributions, n is the number of
discrete values of probability and possibility measures. The coefficients % and & ( %, & >0)
are determined depending on the principles used for transformation. Two transformation
methods are discussed here: a method based on simple normalisation and the more
sophisticated method based on the uncertainty invariance principle .
3.5.1 Transformation by simple normalisation
In this method the power coefficient & (Equation (3.35)) is taken as unity. The
normalisation is required to insure that
(3.36)
(3.27)
Thus, the probability to possibility transformation and the possibility to probability
transformations are given by Equations (3.38) and (3.39), respectively. The advantage of
this method is its simplicity but it lacks a theoretical basis.
(3.38)
(3.39)