An Approach for Medical Diagnosis Based on the Hamming Distances

In medical diagnosis based on intuitionistic fuzzy sets (IFS), it is a general method to use max-min composition based on relations between the symptoms and diseases. The method, however, has been known to lead to quite conservative results and to a loss of information because the composition neglects most values except for extreme ones. To complement the shortcomings of the max-min composition, other measurements such as similarity and distance between IFS have gained attention as an important content in fuzzy mathematics from researchers. However, the methods based on the similarity and distance also have some drawbacks in that they provide an unclear diagnosis. For example, the distances for each disease do not have generally the same distribution. Therefore, there is a difference between the distance 0.25 for disease A and that for disease B. In addition, the difference in the distances for each disease would be very small. It can therefore be inferred that there would be no definite diagnostic criteria. To solve the problems, we propose a new approach for medical diagnosis based on Hamming distances in this study. In the approach, we do not use directly the Hamming distances but the distributional characteristics of the distances such as quantiles and p-values as a measure for diagnosis. To explore the potential for utilization of the approach, we present the simulation results. The simulation was applied to differentiate patients according to the three main types of primary headaches: migraine, tension and cluster headache. The result of the simulation indicates that it is possible to classify headache using the proposed method.