This study proposes a new supervised learning algorithm for probability density functions (PDFs) and effectively applies it to medical images. The proposed algorithm is demonstrated step by step, illustrated with a numerical example, and proofed the convergence. This algorithm contributes significantly to the field of recognition in four key areas. The first contribution is the improvement of determining prior probabilities by establishing a method based on the fuzzy relationship between each classified PDF and groups within the training set through cluster analysis technique. The next contribution involves developing a new measure to evaluate the level of similarity between the classified PDFs and the considered groups. Another contribution is the establishment of a new classification principle, quasi-Bayes, for PDFs. The final contribution of this study is the application of the proposed algorithm to both numerical and image data, where objects are represented as representative PDFs. Practical applications on various medical datasets with different characteristics have demonstrated the outstanding advantages of the proposed algorithm over other methods, including traditional statistics, machine learning, and deep learning approaches, based on metrics such as ACC, AUC, F1-Score, and One-way ANOVA test. Specifically, experimental results of the Skin cancer data show that the proposed algorithm achieved an ACC index of 98.024%, higher than other methods, including ResNet-50, Inception ResNet V2, and CNN with 97.33%, 97.815%, and 80.702%, respectively. Similarly, the proposed algorithm also obtained notable results for other indices such as AUC and F1-Score. Additionally, we also obtained similar results for the Brain tumour dataset.