# Re: Fuzziness as opposed to Probability

From: Robert Ehrlich (bobehrlich@home.com)
Date: Mon Aug 13 2001 - 22:11:57 MET DST

• Next message: Robert Ehrlich: "Re: Fuzziness as opposed to Probability"

Earl:

I believe that some fault can be found in both camps. IMHO unless fuzziness is
equated to "hybridness" - a real observable non volatile property, the
objections from the mathstat camp has some validity.

In other words fuzzy classification makes some sort of sense in a world where
there are peaches (membership =1 cluster 1) plums (membership=1, cluster 2) and
nectarines (membership = .5 in both clusters).

I think that we both agree that the fuzzy domain is qualitatively different from
the statistical domain. If so, many adherents in the fuzzy camp rile people up
when they try to blur the distinction.

Another problem is that sometimes the formal algebraic structures can appear to
be analogous, so people jump to the conclusion that the systems are analogous.
A least squares line of best fit may or may not be a regression line depending
on how I view x and y. Yet to an engineer who doesn't care a hoot about
probabilities, the "non-regression" line of best fit may be of practical value.
so the same algorithm giving the same result need not mean the "same" thing.

Earl Cox wrote:

> Robert,
>
> I agree -- and fuzzy logic is not a solution -- it is a technique. It must
> be used in the proper context and in a well-formed model just like any other
> technique. But I would also point out -- and here I strongly disagree with
> my good friend Will Dwinnell -- fuzzy logic is not a heuristic nor is it an
> approximation to a "better" technique, nor is it a form of regression. Fuzzy
> Logic is based on a solid mathematical foundation and fuzzy systems are
> universal approximators. In modeling many real world phenomena, fuzzy
> systems provide a more robust, less brittle, more easily extensible, and
> more easily tunable approach. Fuzzy systems model the degree to which a
> collection of continuous variables change through an overlaid partitioning
> of (overlaid) semantics. Fuzzy inferencing combines the evidence that a
> solution state is representative of the combined semantics. But I would
> point out that the mechanism of fuzzy inferencing is neither arbitrary,
> ad-hoc, nor related to probability. It has empirical and well formed
> mathematical foundations.
>
> I have been designing and delivering fuzzy models to corporations since
> the early 1980's. Some of the models have risk and failure threat profiles
> in the millions of dollars (such as the models for pharmaceutical companies
> that do high throughput screening of new drugs, the models for managed
> health care fraud detection, etc.) These are not toy models assigned by some
> professor for his/her grad students, but models that my clients have paid
> hundreds of thousands of dollars for and are in use today.
>
> It is distressing, however, for those who build and deliver fuzzy logic
> models to see, year after year after year after year in this news group the
> very same arguments about fuzzy logic and probability or fuzzy logic and
> statistics or fuzzy logic and other cargo cult approaches to warding off
> evil spirits and bad karma. I know this stems almost totally from a lack of
> exposure to real-world fuzzy systems and, in many cases, to professors who
> share a similar bias (based on the same lack of exposure). I would just ask
> how many of the participants in this forum who are arguing about fuzzy logic
> and probability have ever actually read Kosko's two text books on fuzzy
> systems, or Ron Yager's books, or George Klir's wonderfully clear books on
> fuzzy reasoning, or even my own books on real world fuzzy systems? Almost
> none (if not in fact none). I can tell by the very nature of the assertions
> about what you "think" fuzzy is, what it means, and how it works. And, of
> course, I can tell by the scoffing attitude used to discard rules in a real
> fuzzy model that seem contradictory -- without realizing that fuzzy logic
> allows rules that in a Boolean system would definitely be contradictory.
>
> This is the primary reason this news group is so small and so
> intellectually shallow. Look at the robust discussions in the genetic
> algorithm or neural network groups. I don't mean this harshly, I simply mean
> that the entire content of this newsgroup (aside from newbies asking for
> help or Conference notices) is a tiresome, drawn out discussion of the same
> issue year after year. When experienced model builders like Will Dwinnell
> post a few rules from a real world pricing model, the entire group attacks
> the model, attacks the models in my book (from which the rules were drawn)
> and attacks the idea that the model would work. No one even bothered to
> actually think about the fuzzy reasoning underlying these four rules (which
> just happen to be from a real pricing model in daily use since 1987 by a
> British retailer. The actual model has over 120 rules, but the first four
> from the price positioning policy are so difficult to reproduce in an
> ordinary model that I use them in my books and in my seminars.) Another
> group participant actually sent a message saying that his company uses fuzzy
> pricing models successfully and wondered why they haven't caught on.
> Again -- dead silence from the news group.
>
> Benjamin Franklin once remarked that people get the government they
> deserve. This news group gets the participants and the excitement it
> deserves -- and the model builders who dismiss fuzzy logic out of hand
> without any actual knowledge of its real power are getting the tools they
> deserve.
>
> Earl
>
> --
> Earl Cox
> VP, Research/Chief Scientist
> Panacya, Inc.
> Annapolis Junction, MD 20701
> (410) 904-8741
> -------------------------------------------
>
> AUTHOR:
> "The Fuzzy Systems Handbook" (1994)
> "Fuzzy Logic for Business and Industry" (1995)
> "Beyond Humanity: CyberEvolution and Future Minds"
> (1996, with Greg Paul, Paleontologist/Artist)
> "The Fuzzy Systems Handbook, 2nd Ed." (1998)
> "Fuzzy Tools for Data Mining and Knowledge Discovery"
> (due Early Fall, 2001)
>
> "Robert Ehrlich" <bobehrlich@home.com> wrote in message
> news:3B7314D5.9A1FA957@home.com...
> > I am an applied person who uses statistical methods to provide criteria
> for
> > making decisions that may involve a lot of money and their success will be
> > apparent in short order. IMHO neither fuzzy logic, frequentist
> approaches, nor
> > Bayesian approaches ever "prove" anything. They at best raise points that
> must
> > be included in a decision making process. They are most useful when they
> > provide"non common sense" results because it forces us to carefully
> reconsider
> > our understanding of the underlying system. "it is good because it works"
> > strikes me as a circular argument unless there is a real world penalty for
> being
> > wrong. If you are looking for places to drill a 5 megabuck oil well or
> trying
> > to decide whether an occasional death is worth using a new drug things get
> sober
> > quickly and no one says that a numerical result by itself
> > "works". Success is not a good criterion if there is no significant
> penalty for
> > being wrong. Banging on pots always keeps the sun from being eaten by the
> moon
> > during eclipses. it "works" so what?
> >
> > Herman Rubin wrote:
> >
> > > In article <3B69F78D.6020407@bellatlantic.net>,
> > > <predictr@bellatlantic.net> wrote:
> > > >Radford Neal wrote:
> > > >"The whole point of constructing a mathematical formalism for inference
> > > >is to produce conclusions or decisions that are more reliable than
> would
> > > >be produced by unaided human intuition."
> > >
> > > >Will Dwinnell responded:
> > > >"To me, this is the crux of the matter. I don't know about the fine
> > > >point that this statement was in reference to, but I think it expresses
> > > >quite well what I think of as the "engineer's perspective".
> > >
> > > ..................
> > >
> > > >My general question to critics of fuzzy logic in general is: what is
> > > >wrong with using fuzzy logic if it provides useful results?
> > >
> > > ..................
> > >
> > > >Herman Rubin asked:
> > > >"Tell me how to get results."
> > >
> > > >I am not sure what you are asking. The construction of fuzzy logic
> > > >systems is well-described in the literature and I'd refer you to Earl
> > > >Cox's "The Fuzzy Systems Handbook", but I suspect you're asking about
> > > >somthing else?
> > >
> > > >Herman Rubin continues:
> > > >"How does fuzzy logic contribute to getting a consistent scheme of
> action?
> > >
> > > >Can you elaborate on what you mean by a "consistent scheme of action"?
> > >
> > > >Herman Rubin continues:
> > > >"Expectation derived from probability does this. Consistent action has
> > > >been shown to force probability."
> > >
> > > The point is to come up with a procedure for preferences
> > > between actions, so they are not contradictory, and put
> > > this on a quantitative basis so as to go from simple
> > > situations to complicated ones.
> > >
> > > >Herman Rubin, in another message wrote:
> > > >"Complete a "fuzzy" approach in a consistent way, and only probability
> > > >can result."
> > >
> > > >If you are asserting that fuzzy logic, if implemented in some
> > > >appropriate manner must collapse to probability, then you may be right.
> > > >I don't know. But I am not clear on why this would imply that actual
> > > >fuzzy logic systems can't work.
> > >
> > > No, what I am saying is that "fuzziness" will be
> > > incorporated into probability, or it cannot assist in
> > > attaining a course of action. It is that the fuzzicists
> > > collapse probability, not that fuzziness collapses into
> > > probability.
> > > --
> > > This address is for information only. I do not claim that these views
> > > are those of the Statistics Department or of Purdue University.
> > > Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette
> IN47907-1399
> > > hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
> >

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