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Topic: What happened to fuzzy set theory
Replies: 7   Last Post: Jul 7, 2006 7:20 PM

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Toni Lassila

Posts: 536
Registered: 12/13/04
Re: What happened to fuzzy set theory
Posted: Jul 7, 2006 11:44 AM
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On 6 Jul 2006 15:36:27 -0700, "Proginoskes" <CCHeckman@gmail.com>
wrote:

>C6L1V@shaw.ca wrote:
>> ediebur@rcn.com wrote:
>> > Fuzzy set theory was quite popular in the sense that it captured the
>> > popular imagination. I think Japan even built a microprocessor based on
>> > it. What happened?

>>
>> It exploded, It is applied in many areas such as camera focussing,
>> controllers of all types, etc. Just do a simple Google search to see
>> the vast variety of applications that have been suggested or
>> implemented already. Having said that, I must admit that I am still a
>> skeptic. At a conference, I once discussed with a control systems
>> expert the reason why fuzzy controllers are used and sometimes have
>> performance that exceeds that of ordinary controllers. His claim (and I
>> have no independent verification of this) is that fuzzy controllers
>> tend to monitor the system very closely---more closely that typical
>> classical controllers---and so use better estimates of the "state".
>> Their use of better information results in better performance, or so he
>> said.

>
>The only problem is that, in order to get something that works in the
>physical realm, you need to assign specific values to some fuzzy
>concepts. (A concept called "defuzzification".)


Where is the problem? If you design a fuzzy PI controller for a crisp
system then the end result will be equivalent to a conventional PI
controller. It is when the model is imprecise, overly complicated, or
non-existant when the fuzzy controllers stand out from the rest.

I'm not sure that fuzzy controllers beat conventional controllers in
comparison because they "monitor the system very closely", but rather
because they're often compared to linear controllers only. Since the
fuzzy controller is non-linear, it is not surprising that it can in
many cases give better results.

>Fuzzy logic may be the best way to find these values, but in the end,
>we're back at deterministic algorithms.


As mentioned, fuzzy controllers are deterministic. But it seems the
field is somewhat ripe with extraordinary claims as to what model-free
controllers can accomplish. I'd certainly take some things with a
grain of salt. Sort of like with genetic algorithms.



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