A fuzzy probabilistic method for medical diagnosis

The max-min composition in fuzzy set theory has attained reasonable success in medical diagnosis in the past thirty years for estimating the probability of a patient diagnosed with a certain disease. However, there has been no theoretical justification why the method would work. We create a theoretical model to calculate the probabilities of hypothetical patients having designated diseases, and use simulated dataset to explain why the max-min composition has been successful. In addition, based on the theoretical model, we propose a fuzzy probabilistic method to estimate the probability of a patient having a certain disease. The proposed method may produce a more accurate estimate than the max-min composition.