The main aim of this research is to compare two analytical approaches, namely the Dempster-Shafer Method and the Bayes Theorem, in the context of a system developed for diagnosing Moyamoya disease. Moyamoya is a rare condition involving the narrowing or blocking of blood vessels in the brain, which can lead to disrupted blood flow and an increased risk of stroke. In the medical field, diagnosing Moyamoya disease is a crucial initial step for appropriate treatment planning. The Dempster-Shafer Method is an approach used to address uncertainty and combine uncertain information into a conclusion. On the other hand, the Bayes Theorem is a statistical principle that connects the probability of a hypothesis before and after new evidence emerges. Both of these approaches are vital in the medical diagnostic process. In this study, both methods are implemented in an expert system specifically developed for diagnosing Moyamoya disease. Data from Moyamoya cases are used to evaluate the performance of both methods. Performance measurement is conducted by observing diagnostic accuracy, computational time, and resource usage. The results of this research provide valuable insights into the effectiveness and performance of the Dempster-Shafer Method and the Bayes Theorem in medical applications, particularly in diagnosing Moyamoya disease. Strengths and weaknesses of each approach are revealed, aiding in understanding situations where each method is most suitable. The Dempster-Shafer Method is effective in dealing with complex uncertainties and combining uncertain evidence. Meanwhile, the Bayes Theorem excels in probability calculations. The implications of this research are important in developing more advanced medical expert systems. In the medical realm, where diagnostic decisions impact patient care, a better understanding of these approaches helps in selecting the most appropriate method for specific situations. The results of comparing both methods indicate that the Dempster-Shafer Method yields a high probability of around 91%, indicating a substantial likelihood that the patient is suffering from this disease. Conversely, the Bayes Theorem yields a low probability of around 22%, suggesting a relatively small likelihood that the patient has Moyamoya Disease.