# FW: fuzzy number input to a FIS

From: Makropoulos, Christos (c.makropoulos@ic.ac.uk)
Date: Mon Jan 15 2001 - 14:06:41 MET

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> Dear all,
> i was wondering if anybody can answer or point me to publications
>
> How do you handle fuzzy number input in a fuzzy inference system (FIS)
> either type-1 or - prefferably- type-2.
>
> To be more precise, I would like to quantify uncertainty in the input data
> treating each input value of the data set (x) as a fuzzy number with a
> given membership function (i.e. triangular) and a spread (2dx) associated
> with the level of confidence in the particular data set. The data will
> then be passed through a type-2 FIS incorporating uncertainty in the
> inference rules (and the shape of the memebership function(s)).
>
> This is basically a case of trying to assign a membership function to a
> fuzzy number. Can I treat the memebrship function as a crisp mapping
> fuzzy-to-fuzzy and use the extention principle in a number of a-cuts ,
>
> i.e.
>
> {0/(x-dx) + 0.5/(x-dx/2) + 1/x + 0.5/(x+dx/2) + 0/(x+dx)}, the
> fuzzy input data value in 3 a-cuts (0, 0.5, 1)
> m(x) the membership of the fuzzy number to the property in question (say
> "suitability")
> {0/m[(x-dx)] + 0.5/m[(x-dx/2)] + 1/m[x] + 0.5/m[(x+dx/2)] +
> 0/m[(x+dx)]}, the new output value?
>
> In the case of a standard type-1 FIS like matlab's would this practically
> mean that i could pass a vector [x-dx, x-dx/2, x, x+dx/2, x+dx] instead of
> just a point x for every x in my data set and then just assign the [0,
> 0.5, 1, 0.5, 0] membership values of the original fuzzy number to the
> output vector? Is there some inconsistency in my argument?
>
> Additionally, can you point me to any refferences treating data
> uncertainty by fuzzy NUMBERS?
>
> Thank you very very much, ANY hint would be greatly appreciated.
>
> Christos.
>
>
>
>
> ________________________________________________
> christos k. makropoulos
> research assistant
> environmental & water resources engineering
> research group
>
> civil engineering department
> imperial college of science, technology & medicine
> london SW7 2AZ
> united kingdom
> office: ++207-5946018
> fax: ++207-2252716
>
>
>
>

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