Re: Ranking Fuzzy Numbers

I read that some methods use the Center of Gravity of the [Fuzzy
Number/Membership Function] Curve to defuzzify the fuzzy number.
I don't understand how a fuzzy number can be difuzzified by the same
value when the membership function is represented by an equilateral
triangle, a rectangle, or a trabizoid that have a common base.

Dmitry A. Kazakov <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> On 22 Aug 2003 14:21:05 -0700, [EMAIL PROTECTED] wrote:
> 
> >What is the best way to rank fuzzy numers with overalping membership
> >functions to decide the best alternative?
> >i.e. to find out the min or max of a group of fuzzy numbers with
> >overalping membership functions
> 
> x < y and x = y on fuzzy numbers are (as expected) fuzzy propositions.
> So max / min in crisp sense may simply not exist.
> 
> The one thing you can do is to evaluate for each number the
> possibility/necessity that this given number is greater or equal than
> all others from the set. I.e. to make a sort of classification of the
> given numbers as max of the set. To get exactly one number you could
> defuzzify this classification, but this would be rather empiric.
> 
> Another approach is to consider the set of the fuzzy number as a whole
> and to try to find its upper boundary (appropriately defined). The
> result would be also a fuzzy number.
> 
> ---
> Regards,
> Dmitry Kazakov
> www.dmitry-kazakov.de