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From: mackw@bytex.com
Subject: Re: Continuous vs. piecewise-linear MBFs 
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In article <3adrr6$28k@news.tamu.edu>, <vqharral@eesun1.tamu.edu> 
writes:
> Membership functions can arguably be divided into two general 
categories:
> 
>    1. Continuous (e.g. fugoid, gaussian)
>    2. Piecewise-linear (e.g. triangles, trapezoids)
> 
> The "conventional wisdom" where I work is that the piecewise-linear 
variety
> perform just as well as the continuous variety, and that this form 
is used
> in most fuzzy applications because it reduces the complexity of 
evaluating
> the MBFs at virtually no expense in performance.

I can't cite a reference, but I believe the issue is not which 
approach is better, but which approach is easier for your particular 
system to use.  In general, fuzzy set definitions are guesses (okay, 
approximations :-) ), so it is hard to judge which membership shape 
is better.  You hope the membership function has the end points and 
shape about right, but often that is about as far as analysis can 
take you.  If, on the other hand, you have a well defined membership 
function, by all means use it!  Don't throw away information just to 
use the most popular shape.

If anyone out there knows of a method for determining membership 
functions more precisely, please speak up.  I'd love to hear them.

Wayne Mack

