# Re: Arithmetic operations with fuzzy numbers

Tom Whalen (dscthw@panther.Gsu.EDU)
Wed, 20 Nov 1996 01:26:50 +0100

On Wed, 13 Nov 1996, Thomas Hauptmann wrote:
> is there anybody, who can help me in the field of arithmetic operations =
> using fuzzy numbers?
>
> I have to divide two fuzzy numbers (a triangular or trapecial shaped =
> fuzzy number should be divided by a fuzzy number with an EXP-shaped =
> membership-function) and sum up the resulting fuzzy numbers (also =
> EXP-shaped membership-functions).

The approach I would recommend is using fuzzy logarithms. Use the
extension principle to find the fuzzy set of logarithms corresponding to
the two fuzzy numbers, subtract the log of the denominator from the log of
the numerator, and use the extension principle to find the fuzzy set of
antilogarithms corresponding to the result.

Tom Whalen whalen@gsu.edu (404)651-4080 fax (404)651-3498
Professor of Decision Science
The Georgia State University "First things first, but not
Atlanta, GA 30303-3083 USA necessarily in that order" - Dr. Who