In this study, polyester fabric was dyed with madder as an environmentally friendly natural dye. According to Box-Behnken experimental design, 46 samples were dyed under various levels of five parameters including dye concentration, dyebath pH, temperature, time, and liquor ratio, and the color strength (K/S) of the dyed samples was measured. To evaluate the effect of each parameter on the color strength, the data was evaluated using multiple analysis of variance. Then, the artificial neural network (ANN) and fuzzy logic models were used to predict the measured K/S values. As both models contain different parameters, the genetic algorithm was implemented to optimize the model accuracy. It was observed that the best obtained ANN and fuzzy models can predict the K/S values with mean absolute percentage error of 2.52 and 3.01, respectively. Also, the effect of each input parameter on ANN was determined according to the partial derivative method and it was found that the maximum and minimum effects on ANN corresponds to dye concentration and liquor ratio, respectively. Finally, the effects of each dyeing parameter on the color strength was investigated based on the established optimal ANN model.