Goodness-of-Fit Test for Membership Functions with Fuzzy Data

Abstract

Conventionally, we use a chi-square test of homogeneity to determine whether the cell probabilities of a multinomial are equal. However, this process of testing hypotheses is based on the assumption of two-valued logic. If we collect questionnaire data using fuzzy logic, i.e., we record the category data with memberships instead of with a 0-1 type, then the conventional test of goodness-of- t will not work. In this paper, we present a new method, the fuzzy chi-square test, which will enable us to analyze those fuzzy sample data. The new testing process will efficiently solve the problem for which the category data are not integers. Some related properties of the fuzzy multinomial distribution are also described.