# uncertainty estimation?

Subject: uncertainty estimation?
From: Makropoulos, Christos (c.makropoulos@ic.ac.uk)
Date: Sun Oct 01 2000 - 06:45:16 MET DST

dear all,

I am currently using fuzzy sets as a standardization method in multicriteria
spatial analysis. It is the classic GIS problem of suitability maps for
application of specific techniques in "the best location". The technique's
application (in this case water demand management strategies) are dependent
on a number of different criteria and each criterion is standardized with an
"appropriate" fuzzy set membership function. As you very well now there are
several techniques of building a fmf but not much if you cant have field
data: I can claim that a particular part of a network has a 0.8
vulnerability to leakage, but the fact remains that it either leaks or not.
If it doesn't (where the concept of the fmf is applicable) there is no real
way of measuring in-situ the actual vulnerability!.

I have two questions on the subject:
1. How do you built a fmf for say vulnerability to leakage for a water
supply network, due to diameter of the pipe when there is no clear
theoretical function linking them. There is some statistical data simply
saying the small diameters (<300mm) are more vulnerable than large ones and
intermediate diameters are ... intermediate.
2. Say you can built a fmf with a simple shape translating broadly the
statistical evidence I described. It is clear that the shape you choose is
not the only possible one. This would yield a slightly different outcome if
someone else chose another shape: the vulnerability map output would be
different, how is this uncertainty quantifiable??? I know that giving a 0.6
membership is an indirect indication of uncertainty, but I am saying that
this 0.6 is also uncertain to a large extend.

This uncertainty quantification is a major issue in the applicability of
operational maps (suitability, vulnerability, preferable location
identification etc).

Any ideas, references and contacts of this topic of uncertainty
quantification in the use of fuzzy sets will be greatly appreciated!!!

Best Regards

Christos

_____________________________________
christos k. makropoulos

environmental & water resources engineering
research group

civil engineering department
imperial college of science, technology & medicine
london SW7 2AZ
united kingdom

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