# Re: Fuzzy Arithmetic

From: Phil Diamond (pmd@maths.uq.edu.au)
Date: Mon Jan 08 2001 - 12:27:02 MET

• Next message: Kristina Striegnitz: "2nd CfP: ESSLLI 01 Student Session"

In comp.ai.fuzzy you write:

But zero is contained in the support of B, so the support of A/B is
an infinite interval, and so A/B is not a fuzzy number. (If I understand

Cordially, Phil Diamond

>Hello:

>I would like an input from anyone who is familiar with fuzzy
>arithmetic.

>The problem is regarding the division of two trapezoidal fuzzy
>numbers. In some cases I have got incorrect results.
>The formula for the division of two trapezoidal fuzzy numbers (m & n)
>is based on 4 cases:
>1. m > 0 & n > 0; 2. m <0 & n>0; 3. m >0 & n <0; 4. m <0 & n < 0.
>Consider the fuzzy numbers A & B:
>Let A = [0.11 0.2 0.4 0.6] & B=[-0.4 0.2 0.4 0.6]
>The two cases that seem to apply are case 1 and case 3
>Using case 1(m > 0 & n > 0)
>A/B = [0.18 0.5 2.0 -1.5]

>Using case 3(m > 0 & n < 0)
>A/B = [1.0 1.0 1.0 -0.275]

>These are both incorrect. It also raises the question, how does one
>determine if a trapezoidal fuzzy number is negative. Do you think
>finding the crisp average through defuzzification is accurate?

>Cases 2 and 4 (obviously did not apply) also yielded incorrect
>results.

>Clifton

>__________________________________________________
>Do You Yahoo!?
>Yahoo! Photos - Share your holiday photos online!
>http://photos.yahoo.com/

>############################################################################
>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 : Mon Jan 08 2001 - 12:36:11 MET