Re: uncertainty estimation?


Subject: Re: uncertainty estimation?
From: robert john (rij@dmu.ac.uk)
Date: Tue Oct 03 2000 - 18:06:10 MET DST


Other Type-2 Papers:

  John R I (1998) "Type 2 Fuzzy Sets: An Appraisal of Theory and Applications",
International Journal of Uncertainty, Fuzziness and Knowledge Based Systems,
6(6), 563--576.
  John R I and Czarnecki C, (1998) "A Type 2 Adaptive Fuzzy Inferencing System",
Proc. IEEE Systems, Man and Cybernetics'98, 3, 2068--2073.
  John R I, (1998) "Type 2 Fuzzy Sets for Knowledge Representation and
Inferencing", Proc. 7th Intl Conf. on Fuzzy Systems FUZZIEEE '98, 1003--1008.
  John R I, Innocent P R and Barnes M R (1998) "Type 2 Fuzzy Sets and Neuro-Fuzzy
Clustering of Radiographic Tibia Images". Proc. 7th Intl Conf. on Fuzzy
Systems FUZZIEEE '98, 1373--1376.

Ellen Hisdal wrote:

> > 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).
>
> You can find detailed information on Type-N, and especially Type-2, fuzzy sets
> in the paper
>
> @article{ite,
> author = {Hisdal, E.},
> title = {The {IF THEN ELSE} statement and interval-valued fuzzy sets
> of higher type},
> journal = {Int. J. Man-Machine Studies},
> year = {1981},
> volume = {15},
> pages = {385-455},
>
> Greetings,
> Ellen
>
> > Envelope-to: ellen@ifi.uio.no
> > Delivery-date: Mon, 2 Oct 2000 13:09:46 +0200
> > Date: Mon, 2 Oct 2000 12:28:18 +0200 (MET DST)
> > Errors-To: fuzzy-owner@dbai.tuwien.ac.at
> > Reply-To: pramits@vsnl.com
> > Originator: fuzzy-mail@dbai.tuwien.ac.at
> > Sender: fuzzy-mail@dbai.tuwien.ac.at
> > Precedence: bulk
> > From: "P. Sarma" <pramits@vsnl.com>
> > X-Listprocessor-Version: 6.0c -- ListProcessor by Anastasios Kotsikonas
> > X-Comment: Fuzzy Distribution List
> > Content-Transfer-Encoding: 7bit
> > Content-Type: text/plain;
> >
> > 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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> >
> >
>
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> (5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html

--
_______________________________________

Dr R.I. John Department of Computer Science School of Computing Sciences De Montfort University The Gateway Leicester LE1 9BH United Kingdom Work: +44 (0)116 2551551 ext. 8491 Mobile: 07768 174708 Fax: +44 (0)116 2541891

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