Optimizing probabilistic fuzzy systems for classification using metaheuristics

Two new methods for the optimization of probabilistic fuzzy classifiers are proposed. Probabilistic fuzzy systems are specially attractive due to their explicit and simultaneous modelling of two kinds of uncertainty, namely vagueness in linguistic terms (fuzziness) and probabilistic uncertainty. The current method uses the maximization of the likelihood with the stochastic gradient descent, which not only converges to local minima but also does not guarantee the minimization of the misclassification error. The proposed methods address this specific problem by incorporating global search techniques. The first algorithm proposed is a genetic algorithm with simple crossover and mutation operations. The other is a first generation memetic algorithm which combines the genetic algorithm with the stochastic gradient descent. A total of five benchmarks were used to compare the three algorithms. The results show that the proposed methods have an average relative improvement of 2% and 6% for the accuracy with the genetic and memetic algorithms, respectively.