Multiple and partial correlation coefficients of Fuzzy Sets

In many applications, multiple correlation and partial correlation for three or more fuzzy sets are very important, but Chiang and Lin (1999, Fuzzy Sets and Systems 102: 221–226) do not solve this problem. Here, we propose a method to calculate the multiple correlation and partial correlation for fuzzy data, by adopting the concepts from the multivariate correlation model. In order to fit into normal framework, we use empirical logit transform (see, Agresti, [1990, Categorical Data Analysis. New York: Wiley]; Johnson and Wichern, [1992, Applied Multivariate Statistical Analysis 3rd edn. Engelwood Cliffs; Prentice-Hall.]) for membership function grades to achieve this.