Prediction of Color Coordinates of Polyester Fabrics Dyed with Madder Using Mamdani-Fuzzy Logic and Optimization Algorithm

One of the challenges faced by textile engineers has been accurately predicting the color of dyed products. Numerous studies have been conducted in this area thus far. In this paper, the polyester fabrics were dyed using madder, a natural dye, while changing the dyeing process parameters such as the dye concentration, temperature, time, pH, and liquor ratio. Following that, samples’ color coordinates were assessed in terms of L*, a*, and b*. The findings of the statistical analysis demonstrated that all the color data did not fit into a single statistical population; as a result, each color data (L*, a*, and b*) must be taken into account independently for modeling. To this aim, a Mamdani-type fuzzy model was employed and the model parameters, including the number of rules and ranges for each variable, were determined using optimization algorithms such the genetic, particle swarm optimization, and gray wolf optimization. For modeling step, initially, the data were separated into two categories: testing and training. The best models were utilized to predict the test group after being chosen based on their superior performance on the training group. The findings obtained demonstrated that the color coordinate values in terms of L*, a*, and b* could be predicted with an error of 3.05, 1.26, and 2.37, respectively, when a fuzzy model and optimization procedures were used.