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represent uncertainty in P i probabilistically, it is assumed that it bears some error
represented by dimensionless quantities e 1 and e 2 such that 0( e 1 (1 and e 2 !0 . It is also assumed
that the given value of P i is its most credible (or most likely) value represented by P i, mc .
Then two other values minimum, P i ,min , and maximum, P i ,max , are defined as follows:
(5.12)
With these 3 values x mc , x min and x max a triangular MF (Fig. 5.4) is assumed given by
(5.13)
The qualitative meaning of the triangular membership function is the following. The
“true” value of precipitation, P i , is certainly included between P i, min and P i, max and is
likely to be close to P i, mc . The key words are “included” and “close”. These words
constitute the only information that one has about the problem (Revelli and Ridolfi,
2002). By doing so the uncertainty or imprecision associated with the single value of the
forecast precipitation is represented using a fuzzy number on the basis of the minimum
information available about the anticipated precipitation.
Figure 5.4. A triangular membership function with three values: P i, min , P i, mc
and P i ,max .
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