Re: uncertainty estimation?


Subject: Re: uncertainty estimation?
From: Ellen Hisdal (ellen@ifi.uio.no)
Date: Mon Oct 02 2000 - 20:59:31 MET DST


> 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

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> 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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