# Re: Fuzzy Implication Rules with Fuzzy Input

Date: Tue Jan 16 2001 - 03:57:12 MET

• Next message: Vilem Novak: "Re: Fuzzy Implication Rules with Fuzzy Input"

questions:

Dr. Siler wrote:
> True implication operators such as you mention (NOT t-norms) are really
> useless in this situation. The only thing that will work is a t-norm, such as
> Mamdani uses.
Why are they useless? In some articles e.g. Zadeh or
Dubois/Prade have pointed out that for some applications
(especially in expert systems) such operators are needed.

> For example, suppose we have triangular membership functions for small and
> big in rule "If x=small, then y=big". Suppose now that x is a fuzzy
> triangular number with the same width as small, but offset so that in some
> places x is zero but small is not, and in some places small is zero but x is
> not. Then y will be a fuzzy number which is nowhere zero! If you don't
> believe this, try it.
I believe it, or rather I know that this is true. But as I mentioned
before especially Dubois/Prade (e.g. in What are fuzzy rules and
How to use them) justify this fact with their theory of gradual rules
and certainty rules. A fuzzy number or rather a possibility
distribution whose value is nowhere zero bears the information that
every value is possible to a certain degree.

> Don't use an implication operator - use a t-norm.
Aren't there any applications for which you would recommend the
use of implication operators??

Best Regards
Andrej Albert

**********************************
Dipl.-Ing. Andrej Albert
Institut für Massivbau
Alexanderstraße 35
Tel.: 06151/16-7036
Fax : 06151/16-7034
*********************************

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