Fuzzy rule extraction by a genetic algorithm and constrained nonlinear optimization of membership functions

We propose a new method for fuzzy rule extraction from data by a genetic algorithm and a fine tuning of the extracted membership functions by a constrained nonlinear optimization. This approach is able to select the most significant rules out of a set of all possible ones, that is it learns the rule structure by itself. The genetic algorithm does not limit the kind of operator and the number and form of the membership functions for the inputs. However, in order to utilize linear optimization techniques, singletons and center of gravity defuzzification are used on the output side. Since each rule premise may include a conjunction of a variable number of inputs (between one and the input dimension), the "curse of dimensionality" can be overcome, that is the number of rules does not increase exponentially with the input dimension. This feature makes the proposed algorithm especially attractive for interpretation of high dimensional nonlinear mappings that are hard to visualize. The strategy followed by the nonlinear optimization of the fuzzy input membership functions focuses on a good interpretability rather than on best approximation performance. This will be demonstrated on a real world data example.