Similarity measures between type-2 fuzzy sets

In this paper, we give similarity measures between type-2 fuzzy sets and provide the axiom definition and properties of these measures. For practical use, we show how to compute the similarities between Gaussian type-2 fuzzy sets. Yang and Shih's [22] algorithm, a clustering method based on fuzzy relations by beginning with a similarity matrix, is applied to these Gaussian type-2 fuzzy sets by beginning with these similarities. The clustering results are reasonable consisting of a hierarchical tree according to different levels.