Defuzzification?


Subject: Defuzzification?
WSiler@aol.com
Date: Thu Oct 19 2000 - 17:27:56 MET DST


In a message dated 10/18/00 11:52:14 PM Pacific Daylight Time,
ocordero@cti.espol.edu.ec writes:

<< My question is, in general, what do i lose if i defuzzify sets before and
 use crisp values instead of fuzzy sets, what are the pros and cons...?
 thanks. >>

In general, fuzzy systems can output answers to two kinds of questions: (1)
"How much?" and (2) "What?". The answer to (1) is a number; the answer to (2)
is more likely to be a character string or a discrete fuzzy set whose members
are character strings.

Fuzzy control systems almost always always ask "How much?" and expect a
number to be returned. Fuzzy reasoning systems more commonly ask "What?" and
expect a character string in return, for example a classification or
diagnosis.

If we ask "How much?" defuzzification is usually required. But if we ask
"What?", although fuzzification is very often required, defuzzification is
usually not required and is usually undesirable, since ambiguities in output
may result. For example, suppose we have an output fuzzy set of diagnoses
{schizophrenia no_problem bipolar_disorder}, or an output scheme where 1
denotes schizophrenia, 2 denotes no_problem and 3 denotes bipolar_disorder.
We run first our output fuzzy set and get grades of membership
{.7/schizophrenia, .1/no_problem, .8/bipolar_disorder}. We have an obviously
sick patient, but it is uncelar whether the patient has schizophrenia,
bipolar_disorder or both. Now we run scheme 2 and defuzzify, getting 2.0625.
Apparently our patient is practically free of problems, an extremely
misleading answer.

So if we are trying to find out "What?", we should use discrete fuzzy sets
for output (or alternatively a collection of character strings with truth
values attached, and should avoid defuzzification like the plague.

William Siler

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