With a distance of 3.4m, it is classified that 60% is middle, 40% as far and 0% as near. The sum of the individual membership shows just 1 (100%) again, but it has proved as a special practice in control engineering (However 100% isn’t a special point.)
The defined rules are applied to the function grade (μi) determined in the fuzzification at the inference.
The inference of the membership grade for distance (3.4m) is dealt with, and it should be determined how near or far the distance is.
First the processing rules are determined. The rules are mostly based on experiences. For example, WHEN THEN . A set of easy rules could look like the following for ironic distance.
(54) INFERENCE
μA➔ WHEN…THEN. ➔μErgrbnis 1
μB➔ WHEN…THEN. ➔μErgrbnis 2
μC➔ WHEN…THEN. ➔μErgrbnis 3
(55)
a. WHEN Distance is near THEN ironic Distance is far.
b. WHEN Distance is middle THEN ironic Distance is middle.
c. WHEN Distance is far THEN ironic Distance is near.
The measure of how near, middle or far the distance must be becomes the membership grade again.
Then, when conjunctions such as AND, OR etc. appear in the set of rules, an appropriate operator (minimum operator, maximum operator,…) must be selected. In practice, the minimum operator for AND conjunction and the maximum operator for the OR conjunction have proved themselves, because they solve many problems with slight calculation.
Finally, the membership grade of the output subset is calculated. The value of the membership grade is assumed from the premise for the membership grade at the conclusion of that premise. However, an inference rule must exist for each fuzzy set.
(56) a. WHEN distance is middle THEN ironic distance is middle.
IFμmiddle (distance) = 0.6 ➔ μmiddle (ironic distance) = 0.6
(56) b. More premises:
WHEN distance is middle or far THEN ironic distance is near.
IF μmiddle (distance) = 0.6 and μfar (distance) = 0.4
➔ μnear (ironic distance)
= max {μmiddle (distance); μfar (distance)} = max {0.6; 0.4} = 0.6
The maximum operator is selected for the OR conjunction.
花村嘉英（2005）「計算文学入門－Thomas Mannのイロニーはファジィ推論といえるのか？」より英訳 translated by Yoshihisa Hanamura