DNA-binding domains are functional proteins in a cell, which plays a vital role in various essential biological activities. It is desirable to predict and analyze novel proteins from protein sequences only using machine learning approaches. Numerous prediction methods were proposed by identifying informative features and designing effective classifiers. The support vector machine (SVM) is well recognized as an accurate and robust classifier. However, the block-box mechanism of SVM suffers from low interpretability for biologists. It is better to design a prediction method using interpretable features and prediction results. In this study, we propose an interpretable physicochemical property classifier (named iPPC) with an accurate and compact fuzzy rule base using a scatter partition of feature space for DNA-binding data analysis. In designing iPPC, the flexible membership function, fuzzy rule, and physicochemical properties selection are simultaneously optimized. An intelligent genetic algorithm IGA is used to efficiently solve the design problem with a large number of tuning parameters to maximize prediction accuracy, minimize the number of features selected, and minimize the number of fuzzy rules. Using benchmark datasets of DNA-binding domains, iPPC obtains the training accuracy of 81% and test accuracy of 79% with three fuzzy rules and two physicochemical properties. Compared with the decision tree method with a training accuracy of 77%, iPPC has a more compact and interpretable knowledge base. The two physicochemical properties are Number of hydrogen bond donors and Helix-coil equilibrium constant in the AAindex database.