I'm just stating on my Ph.D designing a decision making tool based on L-
fuzzy sets. I share your concerns. Fuzzy sets and techniques based on
them work but the reason for this is far from clear. I am becoming
increasingly convinced that fuzzy sets are a particular example of more
general metrizable topological structures. I think your only defense
for using fuzzy at the moment (it was the one I used in my Master
thsesis) is that it works.
>
>My first question is what can fuzzy logic do UNIQUELY - i.e that no
>other method can do. For example you often hear about the application
>in complex model free systems, and so we can use linguistic knowledge
>- but what about modeling the system using neural networks or even
>*conventional* mathematical numerical based models? Under what
>circumstances will the linguistic knowledge be the ONLY knowledge,
>and why? Is there ANY theoretical PROOF of the uniqueness of
>advantage of fuzzy techniques in controlling complex systems?
>
None that I am aware of short of a mystical waving of the hands.
>Also what is the advantage in using fuzzy logic when it is being
>trained with numerical data. I don't mean to cause offense but I
>often read papers that use fuzzy logic trained with numerical data
>*only* and wonder what was the actual advantage in doing that?
>
I suspect fashion and research funding has a lot to do with it, but
perhaps thats too cynical.
>Lastly but just as importantly, I perceived the main benefit in my
>application was that the system could cope very well with noisy input
>data. I have the experimental results to prove it, and I believe it
>is fundamentally due to the fuzzification of the data, so that noisy
>data may still trigger the same input sets and thus rules as clean
>data. However I would like more solid proof of this, does anyone have
>a reference to a theoretical proof of the ability of fuzzy systems to
>cope with input noise?
>
I think Kosko has tried to prove this but I'm far from convinced.
>Sorry for the length of this letter, I hope you can help me, an I
>thank you for your time.
>
>Adrian
>
I hope this convinces you you're not alone in your difficulty. Some one
asked me if I'd based my fuzzy decision making application on fuzzy
logic and I could only say " If I had it wouldn't have worked"!
Jon Williams
-- Jon Williams