x^2 Test of Goodness of Fit Using Fuzzy Interval Data

Abstract

In some systems which involve the interaction of human beings, such as management systems or social systems, there are cases in which the data includes human vagueness. These data are treated as fuzzy data. Furthermore, to make clear the relation between observed data and the distribution model, the x^2 test of goodness of fit has been used. But, in the case of fuzzy data, this method has to process data ignoring the vagueness, thus causing cases where we obtain incorrect results. In this paper, we propose a method to process the x^2 test of goodness of fit with consideration of the vagueness which is included in the fuzzy data. To investigate its usefulness, our method is applied to test the normality of the observed data, and its usefulness is illustrated using computer simulation.