Adaptation of Membership Functions

The membership functions are defined by the parameters xi, x2, x3 for triangular-shaped membership functions and xi, x2, x3, x4 for trapezoidal membership functions. These parameters are not independent. Additionally the number of parameters can be large when many membership functions are used. In many simulations it could be shown that this strategy is possible but not very effective and often slow.

Another reason to avoid this is that the expert can see these functions quite clearly. This is caused by the experience with the modeled process. It is not the best idea to start a training procedure by changing this sensitive part of a fuzzy system.

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