Re: membership function

From: P. Sarma (pramits@vsnl.com)
Date: Sat Mar 03 2001 - 15:33:17 MET

  • Next message: Larry Hall: "IFSANAFIPS 2001 announcement"

    If the problem is essentially one of good data-fitting (hence good
    curve/surface generation), then there is a nice generic way to look at it.
    This helps at least at the "triage" or selection stage.

    The membership function (MF) set of the FLS is a very close cousin of the
    ANN layer. An RBF-NN, for example starts looking very much like it's cousin
    indeed. The equivalence of the critical fact, that these two (ANN and FLS)
    satisfy the UFA the Weierstrass Approximation Theorem (the famous WAT) is
    intimately theoretically, and practically, linked to the WAT. The
    stand-alone WAT deals with sequences of polynomials.

    With the WAT as hinge, it is intuititive to see that these subset functions
    (of the ANN/FLS) are in fact equivalent to Splines. The activation functions
    of the ANN, and the MF's of the FLS, are parts of splines.

    It is not incorrect to think of the triangular/trapezoidal MF's as linear
    splines, and the others as equivalent curved splines. Modulo inferencing
    operator-selection in the FIE, curves fit better than lines. The selection
    of lines over curves in the FLS MF is often for reasons of

    (1) Lower computational cost, ceteris paribus
    (2) Algebraic tractability - preferable when possible

    -----Original Message-----
    From: Kuentai Chen <kchen@taylor.ie.ksu.edu>
    To: Multiple recipients of list <fuzzy-mail@dbai.tuwien.ac.at>
    Date: Thursday, March 01, 2001 3:07 AM
    Subject: membership function

    >Hello,
    > I have a very basic question for the use of fuzzy logic: If I have a
    >set of data on hand, how do I know what membership to use or if
    >triangular membership function will be good enough?
    > Has any research been done in this field? I would appreciate if
    >anyone can tell me any reference available.
    >Thanks in advance.
    >
    >
    >###########################################################################
    #
    >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
    >
    >
    -----Original Message-----
    From: Kuentai Chen <kchen@taylor.ie.ksu.edu>
    To: Multiple recipients of list <fuzzy-mail@dbai.tuwien.ac.at>
    Date: Thursday, March 01, 2001 3:07 AM
    Subject: membership function

    >Hello,
    > I have a very basic question for the use of fuzzy logic: If I have a
    >set of data on hand, how do I know what membership to use or if
    >triangular membership function will be good enough?
    > Has any research been done in this field? I would appreciate if
    >anyone can tell me any reference available.
    >Thanks in advance.
    >
    >
    >###########################################################################
    #
    >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 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 : Sat Mar 03 2001 - 15:34:51 MET