Analysis of variance for fuzzy data based on permutation method

Abstract

This paper deals with analysis of variance with fuzzy data (ANOVAF) based on permutation method. The permutation method is a nonparametric method introduced by Heap and Johnson for the data when the normal distribution cannot be assumed. We proposed two different approaches to test hypothesis of fuzzy means using the empirical distribution. To compare the results, several distances are considered especially using ρ-distance. Applying Monte Carlo simulation, it is confirmed through the numerical examples that the significant probability (p-value) get approached true parameter (p-value) regardless of distances or testing method based on proposed method. In addition, the number of permutation samples required is determined in the example to satisfy specified given accuracy.