Correlation coefficient for type-2 fuzzy sets

Type-2 fuzzy sets are a generalization of the ordinary fuzzy sets in which each fuzzy set is characterized by a fuzzy membership function. In this article we consider how to define the correlation coefficient between two type-2 fuzzy sets. We have adopted the embedded function model and interpret each type-2 fuzzy set as a weighted ensemble of ordinary fuzzy sets. Using this interpretation enables us to define a correlation coefficient between two type-2 fuzzy sets. (c) 2006 Wiley Periodicals, Inc.