There's a lot of work distributed, here and there, over the literature
on such things. Mizumoto has done a lot of numerical and semi-analytical
work on it (see Fuzzy Control Systems, Kandel and Langholz, eg.).
Semi/numerical results suggest strongly that the modelling similarities
are strong. I am sure many FLS/C researchers might concur - I can
personally verify that FLC's used for some (strongly) nonlinear models
in some of my work consistently show no (easily) discernible difference
for these 2 fuzzy inference models (FIM).
It could be expected that there will be some finite, even if small,
numerical differences. In that case, one could argue that there are
always a large range of free/tuning parameters (eg. MF parameters) in a
FLS/NFLS, to "compensate" for this. In that case, it's generally
(computationally) better to choose the Max-Prod, or Max-Dot FIM. (And,
cite the UFA property as "defense"). The Max-Prod is smooth (Max-Min
causes nonsmooth clipping), and allows easier formulation of, and
solution by, a gradient-like operator for training.
Pramit
-----Original Message-----
From: fuzzy-mail@dbai.tuwien.ac.at [mailto:fuzzy-mail@dbai.tuwien.ac.at]
On Behalf Of Daniel Fortin
Sent: Saturday, March 16, 2002 3:43 AM
To: Multiple recipients of list
Subject: Max-Min Inference and Triangular / Trapezoidal membership
functions
I was wondering if anyone could tell me what the advantages and or
disadvantages of using max-min and max product inferencing are. I'm
using Fuzzy and Neural Approaches in Engineering by Tsoukalas and
Uhrig and it doesn't seem to describe any of the design tradeoffs for
selecting a fuzzy inferencing method. Also, what are the tradeoffs
between using triangular and trapezoidal membership functions?
If anyone could answer these questions I'd really appreciate it.
Thanks in advance!
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