On the Correlations between Fuzzy Variables

The expected value and variance of a fuzzy variable have been well studied in the literature, and they provide important characterizations of the possibility distribution for the fuzzy variable. In this paper, we seek a similar characterization of the joint possibility distribution for a pair of fuzzy variables. In view of the success of introducing the expected value and variance as fuzzy integrals of appropriate functions of single fuzzy variable, it is natural to look to fuzzy integrals of appropriate functions of a pair of fuzzy variables. We consider one such function to obtain the covariance of the pair fuzzy variables and focus on its computation for common possibility distributions. Under mild assumptions, we derive several useful covariance formulas for triangular and trapezoidal fuzzy variables, which have potential applications in quantitative finance problems when we consider the correlations among fuzzy returns.