In head-and-neck radiotherapy, an early detection of patients who will undergo parotid glands shrinkage during the treatment is of primary importance, since this condition has been found to be associated with acute toxicity. In this work, a recently proposed approach, here named Likelihood-Fuzzy Analysis, based on both statistical learning and Fuzzy Logic, is proposed to support the identification of early predictors of parotid shrinkage from Computed Tomography images acquired during radiotherapy. For this purpose, a set of textural image parameters was extracted and considered as candidate of parotid shrinkage prediction; for all these parameters and combinations of maximum three of them, a fuzzy rule base was extracted, gaining very good results in terms of accuracy, sensitivity and specificity. The performance of classification was also compared to a classical Fisher's Linear Discriminant Analysis and found to provide better results. Moreover, the use of Fuzzy Logic allowed obtaining an interpretable description of the relations between textural features and the shrinkage process.