Wang & Mendel

Contrary to the original method [15], this procedure needs predefined fuzzy partitions. They can be automatically generated from data using for instance the Generate a FIS without rules option of the FIS menu.

The prodedure handles all outputs, and ignores existing rules. It needs both a current FIS configuration file and a current data file.

It starts by generating one rule for each data pair of the training set.

The $ i^{th}$ pair one is written :

$ IF  x_1  is  A_1^i  AND  x_2  is  A_2^i  \ldots AND  x_p  is  A_p^i  THEN  y  is C^i$.

The fuzzy sets $ A_j^i$ are those for which the degree of match of $ x_j^i$ is maximum for each input variable $ j$ from pair $ i$. The fuzzy set $ C_i$ is the one for which the degree of match of the observed output, $ y_i$, is maximum.

For a crisp output, an internal conversion creates MFs centered on the output values, then reassigns crisp numbers equal to MF centers to the rule conclusions.

A degree is assigned to each rule. For a given rule it is equal to the rule fire strength for the considered pair. In case of identical premises for two rules, only the one with the higher degree is kept.

This procedure is very easy to use as it does not not require any parameter.

Limitation: this procedure is not well suited to crisp outputs representing continuous numerical values. In that case it can only be used if the observed output has 15 different values or less.