# How is the degree of membership calculated?

CRPFALKSD (crpfalksd@aol.com)
Sun, 26 Apr 1998 22:53:54 +0200 (MET DST)

Question: How is the degree of membership calculated?

Thus far, I understand the basic theories of Fuzzy Logic; however, I am
stumpted by exactly how the degree of membership is calculated. In Bart Kosko's
Book entitled, "Fuzzy Thinking: The New Science of Fuzzy Logic," (which I
thought was a good introductory book) there is an example of Fuzzy Logic
controlling an air conditioner.

In Bart's book, he has this graph (you may want to copy and paste it into

Cool Just Right Warm
1 | /\ /\ /\
| / \ O \ / \
| / \ / \ / \
| / X X \
| / / \ / \ \
| / / O / \ \
0 |/______/_____\/_____\______\_____
45 60 65 70 85

At 63 degrees (noted by the 'O' in the graph), the temperature is 80% (0.80 out
of 1.0) Just Right and 15% (0.15 out of 1.0) Cool. How are these percentages
calculated from 63 degrees? What is the formula for this type of calculation?
Is the Pythagorean formula used in calculating (so long as triangles are used)?

I'm sure it's really simple, and I'm just not seeing it yet. All help
appreciated. :-)

Thanks,
David
crpfalksd@aol.com