From: Arno Dienenthal (A.Dienenthal@iml.fhg.de)
Date: Thu Jan 20 2000 - 13:33:50 MET

I have the feeling that the problem is fomulated in a misleading way. As
far as I know the AND operator in fuzzy reasoning is defined as
"minimum". The OR operator is defined as "maximum".

> (assume that the AND operator is defined as "maximum")
> IF outsideIsGreen AND insideIsRed THEN objectIsWatermelon

IF outsideIsGreen OR insideIsRed THEN objectIsWatermelon

> Suppose we only have 1 fact:
> a certain fruit's outside is 60% green.
> we can conclude that the fruit is a watermelon with possibility 60%

(BTW: the fruit has a watermelon membership of 60%) **

> Suppose we add the following evidence:
> the fruit's inside is red at 40%.
> after recomputing the truth value of the rule, we still get 60%.

> My director says that the possibility should have increased, but
> it did not, so fuzzy logic is not appropriate for this kind of
> reasoning.

I don't really see why it should have increased. Formulating the
condition with the OR operator (keeping the "maximum") makes it clear
that either the first part (outside = green) OR the second part (inside
= red) counts towards the result (object is a watermelon).

** membership is different to possibility. Assume a bottle is deadly
poisonous with probability .1 . Another bottle has a "poisonous"
membership value of .1 . Which one would you drink assuming that a
concentration of less than 20% is without harm for the human body?

Regards
Arno

```--
Arno Dienenthal, M.S.(USA)
Fraunhofer Institut fuer Materialfluß und Logistik (IML)
Abteilung Entsorgungslogistik
Joseph-von-Fraunhofer-Str. 2-4
D-44227 Dortmund
Tel.: +49 (0)231 9743 -347
Fax.: +49 (0)231 9743 -451
e-mail: A.Dienenthal@iml.fhg.de
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