Re: how to combine two fuzzy numbers

From: Dmitry A. Kazakov (mailbox_at_dmitry-kazakov.de)
Date: 09/01/04 

Date: Wed, 1 Sep 2004 19:18:15 +0200

On 30 Aug 2004 13:57:41 -0700, K Yee wrote:

> Suppose I have 2 fuzzy estimates, x and y. For instance, one can imagine they
> are independent predictions of rain by two different forecasters. Suppose I want to
> combine x and y into a "combined" estimate z. What is the formula that optimally
> relates z to x and y?

You can take a look on

http://www.dmitry-kazakov.de/ada/fuzzy.htm

it contains a public domain implementation of fuzzy numbers including
standard arithmetic.

Note that in general there is no simple answer to your answer. Most of the
implementation discard possible dependencies between X and Y. This leads to
less accurate [but still correct] results. Compare it with probabilistic
equivalent: if you know Pr(X=a) and Pr(Y=b) what would be Pr(X+Y=c)? You
cannot tell if you do not know the joint distribution of X and Y. 

-- 
Regards,
Dmitry Kazakov
www.dmitry-kazakov.de