**Previous message:**Gordon D. Pusch: "Re: Do we have proofs that human think in a fuzzy (logic) way?"**Maybe in reply to:**albert@massivbau.tu-darmstadt.de: "Fuzzy Implication Rules with Fuzzy Input"**Next in thread:**Vilem Novak: "Re: Fuzzy Implication Rules with Fuzzy Input"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

This is a comment to Dr. William Silers answer with additional

questions:

Dr. Siler wrote:

*> True implication operators such as you mention (NOT t-norms) are really
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*> useless in this situation. The only thing that will work is a t-norm, such as
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*> Mamdani uses.
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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
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*> big in rule "If x=small, then y=big". Suppose now that x is a fuzzy
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*> triangular number with the same width as small, but offset so that in some
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*> places x is zero but small is not, and in some places small is zero but x is
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*> not. Then y will be a fuzzy number which is nowhere zero! If you don't
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*> believe this, try it.
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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

TU Darmstadt

Alexanderstraße 35

Tel.: 06151/16-7036

Fax : 06151/16-7034

http://www.massivbau.tu-darmstadt.de/user/albert/web/default.htm

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**Next message:**Vilem Novak: "Re: Fuzzy Implication Rules with Fuzzy Input"**Previous message:**Gordon D. Pusch: "Re: Do we have proofs that human think in a fuzzy (logic) way?"**Maybe in reply to:**albert@massivbau.tu-darmstadt.de: "Fuzzy Implication Rules with Fuzzy Input"**Next in thread:**Vilem Novak: "Re: Fuzzy Implication Rules with Fuzzy Input"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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