Combining simplification

Max Polk (maxpolk@gte.net)
Sun, 7 Sep 1997 10:18:13 +0200 (MET DST)

I just finished reading Fuzzy Logic, by Daniel McNeill and Paul
At about the middle of the book they gave an example of how to combine
the suggestions from several fuzzy rules in a fuzzy steam engine
controller.

The concept was to estimate fuzzy set membership, then use the set
membership to limit the portion of a triangle centered around an area of
applicability. By stacking up these triangles with their tops lopped off
and finding the center of gravity, you can defuzzify the output to a
single decision.

I was thinking, instead of using triangles and performing geometrical
addition, as suggested by some source code in books on fuzzy logic
applications in the book stores, why not stack squares at the area of
applicability, as many squares as there are units of fuzzy membership?
That way it would be much easier to determine the center of gravity of
the squares. In fact, it would simply be averaging.

_____
\ ^
\ / \ ___
\____ ___/ \____ ___/ \____
| | |
membership medium medium
applies 0.3 value value truncated
at 0.3 height

Instead of using the result on the right, why not use squares with a
fixed width? That way we would never have to deal with geometric adding.

*
__ *
__/ \ * *
___/ \____ _____*__*___
| |
Find Find
center of center of
gravity DIFFICULT gravity EASILY

The center of gravity for a triangle is always at the middle of the
bottom of the triangle, give the orientation above and assuming an
isoceles triangle. Therefore, simply average to find the center of
gravity rather than fool around with geometric shapes.

Is this correct?