**Previous message:**Rafi Muhanna: "Address Change"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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