In this paper, we present some improvements towards a computational model for colour naming. Our model is based on fuzzy set theory and each colour category is considered a fuzzy set with a characteristic function. In previous works, we had proposed a model based on the use of a Sigmoid-Gaussian as membership function for the chromatic categories. Although it provided good results, the Sigmoid-Gaussian model presents some drawbacks due to the parameter dependence between the Sigmoid and the Gaussian functions. To overcome this, we propose two new functions which are based only on products of Sigmoids avoiding the problems introduced by the Gaussian function. The results obtained by the new functions are compared to the previous ones. Although the improvement in terms of the fitting error is not very significant, the new functions show a higher degree of adaptability which will allow improving the modelling of the whole colour naming space. The functions are also used to label the Munsell colour array and the new membership functions provide similar categorizations than real observers.