In recent years, the high-resolution manometry (HRM) technique has been increasingly used to study esophageal and colonic pressurization and has become a standard routine for discovering mobility disorders. In addition to evolving guidelines for the interpretation of HRM like Chicago, some complexities, such as the dependency of normative reference values on the recording device and other external variables, still remain for medical professions. In this study, a decision support framework is developed to aid the diagnosis of esophageal motility disorders based on HRM data. To abstract HRM data, a new graph-based representation method is introduced that is derived from the spatio-temporal dependencies of pressure values of HRM components. Convolutional graph networks are then utilized to embed relation graphs to the features vector. In the decision-making stage, a novel Expert per Class Fuzzy Classifier (EPC-FC) is presented that employs the ensemble structure and contains expertized sub-classifiers for recognizing a specific disorder. Training sub-classifiers using the negative correlation learning method makes the EPC-FC highly generalizable. Meanwhile, separating the sub-classifiers of each class gives flexibility and interpretability to the structure. The classification results show that our system can distinguish motility disorders with an average accuracy of 78.03% for a single swallow and 92.54% for subject-level classification. Our framework outperforms other comparative classifiers such as SVM and AdaBoost. Moreover, compared with the other studies, the suggested framework has an outstanding performance considering that it imposes no limits on the type of classes or HRM data.