Predicting the colour coordinates of cationic dyeable polyester fabrics dyed with trichromatic combinations of natural colourants using Adaptive Neuro‐Fuzzy Inference System and Sugeno‐type fuzzy logic models

Abstract Easy‐dye cationic dyeable polyester (ECDPET) is a modified easy dyeable polyester that can be dyed using cationic dyes without the need for high temperature or carriers. Dyeing ECDPET with natural dyes further improves the sustainability of the dyeing process. This study involves the preparation of 66 cationic dyeable polyester fabric samples, systematically dyed with varying combinations of madder, Berberis vulgaris root and woad leaves ( Isatis tinctoria ) for red, yellow and blue hues, respectively (ranging from 0% to 100% in 10% increments). The resultant colour coordinates ( L *, a * and b *) for each sample were then precisely measured. Subsequent statistical analyses, comprising ANOVA and multiple comparison tests, definitively established that each colour coordinate corresponds to a distinct statistical population. This finding necessitated the development of separate predictive models for each coordinate. To this end, both Sugeno‐type fuzzy logic and Adaptive Neuro‐Fuzzy Inference System (ANFIS) models were employed. To enhance the predictive accuracy of these models, the genetic algorithm (GA) was utilised for the optimisation of their parameters. The results clearly demonstrated that the ANFIS model exhibited a significantly superior performance compared with the Sugeno model. Moreover, the prediction error for each colour coordinate, when modelled using ANFIS, consistently remained lower than 6%. Therefore, the integration of the ANFIS architecture with GA proves to be an effective methodology for accurately predicting the colour coordinates of polyester fabrics.