Abstract
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.
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The author would like to thank Dr. Anthony B. Mak for several useful discussions.
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This article is part of the Topical on Collection on Systems-Level Quality Improvement
Appendix
Appendix
Physicians sometimes base their decisions on exclusion of certain diseases given the present symptoms [20, 21]
Using the max-min composition, the chance that a patient does not have a certain disease would be given by [20]
In our model, the probability of a patient not having disease d, P p (d’), will be calculated as
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Mak, D.K. A Fuzzy Probabilistic Method for Medical Diagnosis. J Med Syst 39, 26 (2015). https://doi.org/10.1007/s10916-015-0203-9
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DOI: https://doi.org/10.1007/s10916-015-0203-9