Applying Fuzzy Hypothesis Testing to Medical Data

Abstract

Classical statistics and many data mining methods rely on “statistical significance” as a sole criterion for evaluating alternative hypotheses. In this paper, we use a novel, fuzzy logic approach to perform hypothesis testing. The method involves four major steps: hypothesis formulation, data selection (sampling), hypothesis testing (data mining), and decision (results). In the hypothesis formulation step, a null hypothesis and set of alternative hypotheses are created using conjunctive antecedents and consequent functions. In the data selection step, a subset D of the set of all data in the database is chosen as a sample set. This sample should contain enough objects to be representative of the data to a certain degree of satisfaction. In the third step, the fuzzy implication is performed for the data in D for each hypothesis and the results are combined using some aggregation function. These results are used in the final step to determine if the null hypothesis should be accepted or rejected. The method is applied to a real-world data set of medical diagnoses. The automated perception approach is used for comparing the mapping functions of fuzzy hypotheses, tested on different age groups (“young” and “old”). The results are compared to the “crisp” hypothesis testing.