Use of AIC to Select Statistical Models for Fuzzy Interval Data

Abstract

In some systems which involve human beings, such as management systems or social systems, there are cases that we have to treat the data including the haman vagueness. In this paper, these data are treated as fuzzy data, and its probabilities of occurrence are defined by membership functions and statistical models using the definition of Zadeh's probability of fuzzy events. As, also, a ariterion to select a statistical model, AIC (Akaike's Information Criterion) has been defined. However, we cannot obtain AIC directly for a statistical model using fuzzy data. In this papaer, we propose a method to method to select a proper statistical model using AIC from fuzzy data. Using this method, we can select a proper statistical model by selecting a proper distribution model for fuzzy data, and the method extends the area of application of AIC. Furthermore, to investigate the usefulness, our method is applied to the selection problems of parameters of normal distributions, and its usefulness is illustrated using computer simulation.