# Re: Fuzziness as opposed to Probability

From: predictr@bellatlantic.net
Date: Sat Aug 04 2001 - 11:42:04 MET DST

• Next message: Paul Victor Birke: "Re: Fuzziness as opposed to Probability"

Will Dwinnell wrote:

"Here is a simple fuzzy logic system, borrowed from an example given in
"The Fuzzy Systems Handbook", by Earl Cox. The problem is to establish
the price of a product. The fuzzy system has 4 rules:

1. The price should be high
2. The price must be low
3. The price must be around 2 times cost
4. If the competition price is not very high, then the price should be
near the competition price

Mathematical definitions terms like "high", "low", "near the competition
price" etc. are part of this fuzzy system, which yields a suggested
price. These rules are in fact part of a system which has been used to
price millions of dollars worth of real products for a profit-making
enterprise. This fuzzy system solves the problem for which it was intended.

My question to fuzzy critics is: why should this system not be used?"

Rich Ulrich responded:
"I stopped by the library and thumbed through Cox's book. I checked out
a book of "Practical applications ..." instead, because Cox's seemed to
be filled with toy problems.
The example above doesn't seem very serious, either."

I'm not clear on whether you're criticizing the stated problem, which is
a very serious one faced by real companies, or the provided solution,
which has been found in practice to be an effective one. Regardless,
neither is relevant to my question about fuzzy logic as the
underpinnings of the model.

Rich Ulrich continues:
"Let me see: My answer starts with tossing out (1) and (2) as, not only
fuzzy but directly in conflict. Then I settle for round numbers.

a) Set the price at the average of
< competitor's price > and < 2 times cost > if those quantities are not
more than 25% apart.

b) If they are farther apart, scream for help.

Yours seems like plausible alternative, which would of course require
further testing before being put into use. But this still doesn't get
to my question about the appropriateness of using fuzzy logic as the
inference mechanism.

Rich Ulrich continues:
"I said before, something like, commercial solutions I've heard of were
(it seemed) victories for glib salesmen, not for science."

I'm not clear as to how this is material to the issue at hand.

Rich Ulrich continues:
"Is the "fuzzy" answer more precise than mine?"

This question could only be answered by practical testing within the
context of the problem.

Rich Ulrich continues:
"Does the fuzzy answer include a warning/diagnostic against
heterogeneity, that plays the role of my (b)?"

This would depend on the specifics of the implementation.

Will Dwinnell
predictor@dwinnell.com

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