Comparison of Two Interval Models for Fuzzy-Valued Genetic Algorithm

Abstract

Genetic algorithm (GA) employs real numbers (or bit strings) as genotype values for solving real-valued optimization problems. The author previously proposed an extension of GA. The proposed method extends the processes of GA to handle fuzzy numbers as genotype values so that GA can be applied to fuzzy-valued optimization problems. The author has applied the FGA to the evolution of fuzzy-valued neural networks (FNN) and showed that FGA could evolve FNNs, which model fuzzy functions well, despite that the training (evolution) of the FNNs was not supervised. In the previous paper, fuzzy numbers as the genotype values were symmetric triangular ones. Each symmetric triangular fuzzy number can be specified by its lower and upper limit values or its center and width values, and thus the FGA can employ either of two models, the lower and upper (LU) model or the center and width (CW) model for specifying genotype values. Ability of the FGA in searching solutions may depend on the model, because the crossover and the mutation operations for the fuzzy genotypes with the LU model are slightly different from those operations with the CW model. In this paper, the author compares the two models to investigate which model contributes better for the FGA to find better solutions. Application of the FGA is evolutionary training of the FNNs. An experimental result shows that the CW model contributed slightly better than the LU model in evolving FNNs which model fuzzy functions.