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About Fuzzy Control
Minimax Load-Center Method
At the earlier stage of Fuzzy control, Mamdani’s [Minimax Load-Center] method had been exclusively applied. Its inference logic takes the following steps.
- Seeks the intersections [a, b] (grade) of the membership functions [A, B] (grade = 1 Max.) and the external inputs [x1, x2] for each rule at the antecedent sector, then selects the minimum value [a] or [b].
- Applies the minimum value [a] or [b] sought in the step-1 to cut the upper part of the membership functions (Triangle) at the consequent sector, then creates the trapezoid with a height of [a] or [b].
- Repeats the step-1 and step-2 for all rules.
- Superpose all trapezoids created at the consequent sector and seeks the maximum envelope shape.
- Computes the load-center [Z0] as a result of the inference based on the maximum envelope shape sought in the step-4.
- The mathematical presentation of the above steps are shown here.
This inference method is not suitable to the human intuition in most of the cases as well as it is very difficult to analyze its inference result. Due to use of the maximum envelop, some originally effective inference results are ignored (The rule-3’s result is completely hidden within the envelope of the rule-2’s and rule-3’s results). Due to use of the minimum values of the inputs, the other input data also become useless. As a result, the sensitivity of control is adversely affected. This inference method also makes it hard to tune the Fuzzy rules since it employs a rather nonlinear model computation with the minimax relationship between the inputs and outputs.
Minimax Load-Center Method Illustration
Ant. (Antecedent) = Input sector / Consq. (Consequent) = Output sector
 (C) 2004 ADWIN Corp.
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