Newsgroups: comp.ai.fuzzy
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From: bytex!pc_mail!mackw@uunet.uu.net (MACKW)
Message-ID: <9410101025.A23283@pc_mail>
Subject: Center of Mass - Conceptual Question
Date: Mon, 10 Oct 94 10:25:09 EST
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I have a basic conceptual question concerning how operations
are done in fuzzy logic.  Could anyone provide some insights
as to the following?

In a fuzzy rule, why is a point on the input subset curve
translated into an attenuated area under the output subset
curve?  Next a center of mass calculation is used to convert
from the output subset area to a point on the output subset
curve.  One side effect of this approach is for a single rule
example, ala "if A then B", the center of mass of B never
changes and output B is independent of input A.  For example:

     if     A       then      B  

     |      +           |
     |     / \__________|_____
     |    /  |\         |    / \
     |   /   | \        |   /   \
     |  /    |  \       |  /     \
     +--------------    +------------
                              ^
                              |
                        Always the center of mass.

I understand how to do this process, I just am unclear as to
why it is done this way.  It's been a while since I've had
college math, so if you could target the answer for the simple
minded, I would appreciate it! :-)

Wayne Mack (mackw@bytex.com)
Bytex Corp.

