Test of distribution type by likelihood ratio based on fuzzy interval data

In some systems which involve human beings, such as management systems or social systems, there are cases that if we can observe the data with human vagueness then the observation becomes easy. Then, the methods which treat these data as fuzzy interval data have been proposed. On the other hand, to investigate the distribution type of observed data, the test of statistical hypothesis has been used. For this purpose, we use the likelihood ratio test in this paper. But, when we treat the fuzzy interval data, the method for usual data has to process the data in which the vagueness is ignored, and there are cases that we obtain the incorrect result by that method. Then, in this paper, we propose the method to process the vague data for likelihood ratio test by considering the vagueness which is included in the fuzzy interval data. Furthermore, we apply our method to the test of distribution type, and its usefulness is illustrated using computer simulation.