**Subject: **Re: uncertainty estimation?

**From: **P. Sarma (*pramits@vsnl.com*)

**Date: **Mon Oct 02 2000 - 12:30:33 MET DST

**sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**robert_wilhelm_land: "Grid-partitioning Fuzzy Systems"**Previous message:**Hassan M. Chawiche: "Papers"**Maybe in reply to:**Makropoulos, Christos: "uncertainty estimation?"**Next in thread:**Ellen Hisdal: "Re: uncertainty estimation?"**Maybe reply:**P. Sarma: "Re: uncertainty estimation?"

Usual fuzzy sets capture a single level of vagueness or imprecision.

Extremely noisy data-sets, or sets with the large qualitative ambiguities

seen from the examples then pose the question of higher order uncertainty

(HOU). There are at least two different ways to handle this HOU data. One

way, conceptually, is to hybridise different representations. These

representations may be chosen, for example, using a minimal a priori

knowledge. In fuzzy control, for example, it may be fruitful to capture

noisy HOU data using a hybrid of random and fuzzy variables. It is known by

the domain experts here that the additional uncertainty has a probabilistic

nature.

In the absence of such a priori uncertainty classification, the more general

case is perhaps best handled by the hierarchical higher order fuzzy

representation. These were defined conceptually in the same sweep as the

basis fuzzy set (FS) paper by Zadeh. They are called Type-N Fuzzy Sets ...

and the first important extension of the regular (Type-1) fuzzy set is then

the Type-2 set. The regular FS, by definition, has a crisp-valued collection

of MF's. For Type-2, the MF of each fuzzy term is itself fuzzy, and is

defined by an appropriate fuzzy subset. The capture, or identification, of

data is then processed in a way that naturally extends the Type-1

procedures. This is a direct consequence of a recursive application of the

Zadeh Extension Principle.

Information on Type-N, often Type-2, FS may be found here and there in the

general FS literature (Fuzzy Sets & Systems, IEEE Trans. Fuzzy Systems inter

alia).

Pramit

-----Original Message-----

From: Makropoulos, Christos <c.makropoulos@ic.ac.uk>

To: Multiple recipients of list <fuzzy-mail@dbai.tuwien.ac.at>

Date: Saturday, September 30, 2000 1:48 AM

Subject: uncertainty estimation?

*>> 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!!!
*

*>>
*

*>> Thanks in advance
*

*>> 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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*>
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**Next message:**robert_wilhelm_land: "Grid-partitioning Fuzzy Systems"**Previous message:**Hassan M. Chawiche: "Papers"**Maybe in reply to:**Makropoulos, Christos: "uncertainty estimation?"**Next in thread:**Ellen Hisdal: "Re: uncertainty estimation?"**Maybe reply:**P. Sarma: "Re: uncertainty estimation?"

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