Re: Fuzzy * Fuzzy

From: Ellen Hisdal (ellen@ifi.uio.no)
Date: Sun Feb 11 2001 - 07:48:06 MET

  • Next message: Alexander Podvesovsky: "Re: Fuzzy * Fuzzy"

    Dear Otto,

    The following is a reference to a paper treating fuzzy subsets of type 2.
    A fuzzy subset of type 2 is a subsets of a universe V.
    However its grades of membership values are not numerical values in [0,1],
    but fuzzy values (fuzzy subsets of [0,1]).

    If one wishes, one can denote these values
    linguistically by such words as `high', `low' `very high', etc.
    Section 3 of this paper also defines the operations of union and
    intersection on such fuzzy sets of type 2.

    See section 3 of:
    @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},
       ignored = {figure 15, page 426 for wrong inference from Zadehs IF THEN.
                  section 2, page 389 implication versus IF THEN}
                                    }

    I do not know of any papers which use fuzzy values on the abscissa
    axis of the membership function.

    Best greetings,
                       Ellen

    P.S. If you have difficulties in obtaining a copy of the
    International Journal of Man-Machine Studies, I can mail you a reprint.

    ---------------------------------------------------------------------
    Address, etc.:
           Ellen Hisdal | Email: ellen@ifi.uio.no
           (Professor Emeritus) |
    Mail: Department of Informatics | Fax: +47 22 85 24 01
           University of Oslo | Tel: (office): 47 22 85 24 39
           Box 1080 Blindern |
           0316 Oslo, Norway | Tel: (secr.): 47 22 85 24 10
    Location: Gaustadalleen 23, |
           Oslo | Tel: (home): 47 22 49 56 53
    ---------------------------------------------------------------------

    P.S. If you have difficulties in obtaining a copy of the
    International Journal of Man-Machine Studies, I can send you a reprint.

    > Envelope-to: ellen@ifi.uio.no
    > Delivery-date: Thu, 8 Feb 2001 17:42:22 +0100
    > Date: Thu, 8 Feb 2001 17:38:52 +0100 (MET)
    > Errors-To: fuzzy-owner@dbai.tuwien.ac.at
    > Reply-To: ocordero@cti.espol.edu.ec
    > Originator: fuzzy-mail@dbai.tuwien.ac.at
    > Sender: fuzzy-mail@dbai.tuwien.ac.at
    > Precedence: bulk
    > From: "Otto Cordero" <ocordero@cti.espol.edu.ec>
    > X-Listprocessor-Version: 6.0c -- ListProcessor by Anastasios Kotsikonas
    > X-Comment: Fuzzy Distribution List
    > Content-Type: text/plain;
    > Content-Transfer-Encoding: 7bit
    >
    > Dear All:
    >
    > A generic membership functions has the form [x1, x2] --> [y1, y2], where x1,
    > x2, y1 and y2 are real numbers in most of the cases. I am interested in
    > those particular cases where the axis of the membership function are not
    > crisp but fuzzy (for example: if [x1, x2] or [y1, y2] are fuzzy intervals or
    > if their elements are fuzzy numbers).
    >
    > I would appreciate if you point out any publication regarding the
    > mathematical treatement of this kind of membership functions defined in
    > terms of fuzzy elements.
    >
    > Otto Cordero
    > ocordero@cti.espol.edu.ec
    >
    >
    > ############################################################################
    > 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 : Sun Feb 11 2001 - 07:58:50 MET