Re: uncertainty estimation?


Subject: Re: uncertainty estimation?
From: P. Sarma (pramits@vsnl.com)
Date: Mon Oct 02 2000 - 12:30:33 MET DST


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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