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

• Next message: Nikitas Assimakopoulos: "Special Issue of JASS journal"

This is a multi-part message in MIME format.

------=_NextPart_000_001F_01C0D3B4.5F79B680
Content-Type: text/plain;
charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable

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?

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
------=_NextPart_000_001F_01C0D3B4.5F79B680
Content-Type: text/html;
charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<META content=3D"text/html; charset=3Dwindows-1252" =
http-equiv=3DContent-Type>
<META content=3D"MSHTML 5.00.2920.0" name=3DGENERATOR>
<STYLE></STYLE>
<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?!, =
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 =
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>
------=_NextPart_000_001F_01C0D3B4.5F79B680--
############################################################################
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 May 07 2001 - 02:03:09 MET DST