following four fuzzy subsets to


following four fuzzy subsets to z:

, x = 0.0 y = 3.2. z:

rule1(z) = { z / 10, if z <= 6.8

0.68, if z >= 6.8 }

rule2(z) = { 0.32, if z <= 6.8

1 - z / 10, if z >= 6.8 }

rule3(z) = 0.0

rule4(z) = 0.0

MAX composition would result in the fuzzy subset:

:

fuzzy(z) = { 0.32, if z <= 3.2

z / 10, if 3.2 <= z <= 6.8

0.68, if z >= 6.8 }

PRODUCT inferencing would assign the following four fuzzy subsets to z:

z:

rule1(z) = 0.068 * z

rule2(z) = 0.32 - 0.032 * z

rule3(z) = 0.0

rule4(z) = 0.0

SUM composition would result in the fuzzy subset:

:

fuzzy(z) = 0.32 + 0.036 * z

Sometimes it is useful to just examine the fuzzy subsets that are the

result of the composition process, but more often, this FUZZY VALUE needs

to be converted to a single number -- a CRISP VALUE. This is what the

defuzzification subprocess does.

, , , - . - , .

There are more defuzzification methods than you can shake a stick at. A

couple of years ago, Mizumoto did a short paper that compared about ten

defuzzification methods. Two of the more common techniques are the

CENTROID and MAXIMUM methods. In the CENTROID method, the crisp value of


    





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