About Fuzzy Control

Linear Fuzzy Inference Method

1. 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 multiplies the values [a] and [b] to seek its product [m]. m = a x b
2. Retrieves the contribution rate [c] which can be randomly preset for each rule. It is usually set to [1.0] as a reference value. To increase the contribution rate, it can be preset to [9.9] at maximum. To decrease, on the contrary, it is [0.1] at minimum since the rule does not work if it is preset to [0.0].
3. Multiplies the values [m] and [c] to seek its product [mm]. mm = m x c
4. Outputs the grade [mm] at its preset label position [Z].
5. Repeats the step-1 and step-4 for all rules.
6. Adds all grades at the same label position [Z] in the consequent sector.
7. Computes the load-center [Z0] as a result of the inference.
8. 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.

Linear Fuzzy Inference Method Illustration
Ant. (Antecedent) = Input sector / Consq. (Consequent) = Output sector

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