Re: Defuzzification?


Subject: Re: Defuzzification?
From: Paul Victor Birke (nonlinear@home.com)
Date: Fri Oct 20 2000 - 16:33:42 MET DST


WSiler@aol.com wrote:
>
> 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.
************************************

Dear William

While the traditional answer to [1] is a single crisp number work on
Pricing and Markets some years back convinced me otherwise. I view many
Fuzzy Functions as in reality Ultra Fuzzy Functions. Here the Bandwidth
could be zero resulting in a single crisp number. However, many times
the Bandwidth is non-zero. I have assumed a Uniform Distribution across
the Bandwidth of the Ultra Fuzzy Function. So what actually is reported
is an interval set {LOW,HIGH} wherein it is equally possible to find the
number in that interval but NOT outside.

Therefore, Defuzzification generally implies an interval of two crisp
values, LOW & HIGH.

Paul V. Birke, P. Eng.
NN Researcher in Guelph ON CANADA

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