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From: RAHNJ@vm1.ulaval.ca (Joel Rahn)
Subject: Re: Continuous vs. piecewise-linear MBFs
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Date: Fri, 18 Nov 1994 21:07:16 GMT
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In article <3adrr6$28k@news.tamu.edu>
vqharral@eesun1.tamu.edu (Vance Quinton Harral) writes:
 
>Hello Netters,
>
>Membership functions can arguably be divided into two general categories:
>
>
>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.
>
>However, despite the fact that all the people I have asked seem to prefer
>the piecewise-linear variety, noone has been able to quote a textbook or
>journal article which formally makes the claim that these MBFs are "just
>as good" as continuous MBFs.
>
>Does anyone know of such a reference?
>
>
I know a reference exists; I just can't put my hands on it. It came from
a conference paper in Italy, last year and was referenced in an article
about fuzzy controllers in Systems, Man and Cybernetics this year (I
think). In any case, it proved that triangular mbfs are sufficient to
represent any nl control sufficiently closely; i.e. they are in a sense
complete. I'll look some more to pin down the reference if I can.
 
