Re: fuzzy equations and linear systems of equations

From: Rafi Muhanna (rafi.muhanna@gtrep.gatech.edu)
Date: Mon May 07 2001 - 01:59:02 MET DST

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    Silvia wrote:

    "Do you have any reference about fuzzy equations and fuzzy linear system =
    of
    equations of the type Ax=3Db?
    If A is a fuzzy matrix and b is a crisp vector, then are there =
    solutions?
    Thank you for your help"

    This question is well discussed in any Interval Arithmetic book ( a =
    fuzzy
    number could be considered as nested intervals), For example:

    1. Methods and Applications of Interval Analysis, Ramon E. Moore,
    SIAM,1979.
    2. Interval methods for systems of equations, Arnold Neumaier, =
    Cambridge
    University Press 1990.

    However, special attention should be paid to the dependency problem?!, =
    some
    additional developments have been done in this area.

    Beast regards,

    Rafi Muhanna
    -------------------------------------------------------------------------=

    ---
    -----
    Rafi L. Muhanna
    

    Department of Civil Engineering Regional Engineering Program Georgia Institute of Technology

    6001 Chatham Center Dr., Suite 350 Savannah, GA 31405 USA

    Email: rafi.muhanna@gtrep.gatech.edu Phone: (912) 651-7547 Fax: (912) 651-7279

    ----- Original Message ----- From: "Silvia Muzzioli" <s.muzzioli@unimo.it> To: "Multiple recipients of list" <fuzzy-mail@dbai.tuwien.ac.at> Sent: Tuesday, April 03, 2001 6:59 PM Subject: fuzzy equations and linear systems of equations

    > Dear all, > do you have any reference about fuzzy equations and fuzzy linear = system of > equations of the type Ax=3Db? > If A is a fuzzy matrix and b is a crisp vector, then are there = solutions? > Thank you for your help > Silvia

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    <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META content=3D"text/html; charset=3Dwindows-1252" = http-equiv=3DContent-Type> <META content=3D"MSHTML 5.00.2920.0" name=3DGENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=3D#ffffff> <DIV><FONT face=3DArial size=3D2>Silvia wrote:<BR><BR>"Do you have any = reference=20 about fuzzy equations and fuzzy linear system of<BR>equations of the = type=20 Ax=3Db?<BR>If A is a fuzzy matrix and b is a crisp vector, then are = there=20 solutions?<BR>Thank you for your help"<BR><BR>This question is well = discussed in=20 any Interval Arithmetic book ( a fuzzy<BR>number could be considered = as&nbsp;=20 nested intervals), For example:<BR><BR>1.&nbsp;&nbsp;&nbsp; Methods and=20 Applications of Interval Analysis, Ramon E.=20 Moore,<BR>SIAM,1979.<BR>2.&nbsp;&nbsp;&nbsp; Interval methods for = systems of=20 equations, Arnold Neumaier, Cambridge<BR>University Press = 1990.<BR><BR>However,=20 special attention should be paid to the dependency problem?!, = some<BR>additional=20 developments have been done in this area.<BR><BR>Beast = regards,<BR><BR>Rafi=20 Muhanna<BR>--------------------------------------------------------------= --------------<BR>-----<BR>Rafi=20 L. Muhanna<BR><BR>Department of Civil Engineering<BR>Regional = Engineering=20 Program<BR>Georgia Institute of Technology<BR><BR>6001 Chatham Center = Dr., Suite=20 350<BR>Savannah, GA=20 31405<BR>USA<BR><BR>Email:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp= ; <A=20 href=3D"mailto:rafi.muhanna@gtrep.gatech.edu">rafi.muhanna@gtrep.gatech.e= du</A><BR>Phone:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=20 (912)=20 651-7547<BR>Fax:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb= sp;=20 (912) 651-7279<BR><BR>----- Original Message -----<BR>From: "Silvia = Muzzioli"=20 &lt;<A = href=3D"mailto:s.muzzioli@unimo.it">s.muzzioli@unimo.it</A>&gt;<BR>To:=20 "Multiple recipients of list" &lt;<A=20 href=3D"mailto:fuzzy-mail@dbai.tuwien.ac.at">fuzzy-mail@dbai.tuwien.ac.at= </A>&gt;<BR>Sent:=20 Tuesday, April 03, 2001 6:59 PM<BR>Subject: fuzzy equations and linear = systems=20 of equations<BR><BR><BR>&gt; Dear all,<BR>&gt; do you have any reference = about=20 fuzzy equations and fuzzy linear system of<BR>&gt; equations of the type =

    Ax=3Db?<BR>&gt; If A is a fuzzy matrix and b is a crisp vector, then are = there=20 solutions?<BR>&gt; Thank you for your help<BR>&gt;=20 Silvia<BR></FONT></DIV></BODY></HTML>

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