Mamdanisääntöjä

Mamdani's Inference Method, commonly referred to as Mamdani's rule of thumb, is a widely used approach in fuzzy logic control systems. It was developed by Ebrahim Mamdani and his colleagues in 1975. The method is particularly useful in scenarios where the system's behavior is difficult to model mathematically, but expert knowledge is available.

The Mamdani method operates on fuzzy sets, which are sets whose elements have degrees of membership. These fuzzy sets are defined by membership functions that map inputs to degrees of membership between 0 and 1. The method involves several steps: fuzzification, rule evaluation, aggregation of the rule outputs, and defuzzification.

In the fuzzification step, crisp inputs are converted into fuzzy sets. These fuzzy sets are then used to evaluate the rules in the rule base. Each rule in the rule base has the form "IF x is A THEN y is B," where A and B are fuzzy sets. The degree to which the rule is satisfied is determined by the minimum of the degrees of membership of the input fuzzy sets.

The outputs of the rules are then aggregated to form a single fuzzy set. This is typically done using the maximum operator, which takes the maximum degree of membership for each output fuzzy set.

Finally, the aggregated fuzzy set is defuzzified to produce a crisp output. This is done using a defuzzification method, such as the centroid method, which calculates the center of mass of the aggregated fuzzy set.

The Mamdani method is intuitive and easy to implement, making it a popular choice for fuzzy logic control systems. However, it can be computationally intensive, especially for systems with a large number of rules. Despite this, it remains a fundamental technique in the field of fuzzy logic.