FW: fuzzy number input to a FIS

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

  • Next message: Daphne Koller: "UAI-01 Call for Papers"

    > Dear all,
    > i was wondering if anybody can answer or point me to publications
    > answering the following question:
    >
    > 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
    >
    >
    >
    >

    ############################################################################
    This message was posted through the fuzzy mailing list.
    (1) To subscribe to this mailing list, send a message body of
    "SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at
    (2) To unsubscribe from this mailing list, send a message body of
    "UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com"
    to listproc@dbai.tuwien.ac.at
    (3) To reach the human who maintains the list, send mail to
    fuzzy-owner@dbai.tuwien.ac.at
    (4) WWW access and other information on Fuzzy Sets and Logic see
    http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info
    (5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html



    This archive was generated by hypermail 2b30 : Mon Jan 15 2001 - 14:18:09 MET