On possibilistic correlation

Abstract

In 2004, Fullér and Majlender introduced the notion of covariance between fuzzy numbers by their joint possibility distribution to measure the degree to which they interact. Based on this approach, in this paper we will present the concept of possibilistic correlation representing an average degree of interaction between marginal distributions of a joint possibility distribution as compared to their respective dispersions. Moreover, we will formulate the classical Cauchy–Schwarz inequality in this possibilistic environment and show that the measure of possibilistic correlation satisfies the same property as its probabilistic counterpart. In particular, applying the idea of transforming level sets of possibility distributions into uniform probability distributions, we will point out a fundamental relationship between our proposed possibilistic approach and the classical probabilistic approach to measuring correlation.