Re: Beginners question

On 6 Jun 2006 05:50:39 -0700, Hadi Asghari wrote:

Dmitry A. Kazakov wrote:
In my view, the activation function, and/or operators and defuzzification
are determined by the problem space. When you take PROD and SUM you
silently assume that the truth values behave as probabilities of independent events.

Where can I find more information on this?

If you ask about probabilities and additive measure, then any book on
mathematical statistics would fit. If you mean applicability of, then there
are quite clear requirements. For example, you need the sigma algebra,
random variables etc. The reason why PROD and SUM aren't working is that
probably these requirements are not satisfied. If they worked, I would
suggested to abandon fuzzy and do it statistically. Maybe you can describe
it statistically, maybe not. Same is true for fuzzy based on min/max/1-x,
though fuzzy require less premises to be satisfied. Min/max is justified by
the possibility theory (see Dubois & Prade books).

--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
.

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