Measurement and valuation of a fuzzy mathematical model for medical diagnosis

Abstract

Classical mathematical models for medical diagnosis which have been computerized are known to perform very poorly when compared to diagnoses made by the physician. Factors which contribute to their poor performance relate to the omission by these models of important information on the patient such as symptoms of past undiagnosed diseases which can only be vaguely recalled by the patient. Other deficiencies include failure to model the stage of development of the disease, and certain intrinsically fuzzy aspects of the pertinent information nets that are needed to develop a medical hypothesis. Models which attempted to remedy these shortcomings were developed and presented by the authors elsewhere. In this effort, we describe a study in which our fuzzy diagnosis models were computerized, validated and compared with a mock physician hypothesis as well as existing mathematical models. The example involved a medical hypothesis concerning a medical condition of valvular heart disease. The fuzzy sets together with their membership functions were measured using a distance criterion measure similar to the one employed by Kochen to quantify fuzzy adjectives in psychology. The results show that while there were discrepancies between the fuzzy model's and the physician's hypotheses, the model's performance was vastly superior to that of existing mathematical models. While the fuzzy models did well in naming the diseases, they performed less satisfactorily in the specification of the disease stage development, a factor completely ignored by classical models. Improvement in measurement aspects and the choice of diseases possessing discriminant attributes will greatly increase the accuracy of these models. It is however shown that a fuzzy systems approach is not only practical but results in models of greater validity than those based on classical set theoretic approaches.