Some applications of possibilistic mean value, variance, covariance and correlation

In 2001 we introduced the notions of possibilistic mean value and variance of fuzzy numbers. In this paper we list some works that use these notions. We shall mention some application areas as well. 1 Possibilistic mean value, variance, covariance and correlation A fuzzy number A is a fuzzy set R with a normal, fuzzy convex and continuous membership function of bounded support. The family of fuzzy numbers is denoted by F . Fuzzy numbers can be considered as possibility distributions [11, 15]. A fuzzy set C in R2 is said to be a joint possibility distribution of fuzzy numbers A,B ∈ F , if it satisfies the relationships max{x | C(x, y)} = B(y) and max{y | C(x, y)} = A(x) for all x, y ∈ R. Furthermore, A and B are called the marginal possibility distributions of C. Let A ∈ F be fuzzy number with a γ-level set denoted by [A]γ = [a1(γ), a2(γ)], γ ∈ [0, 1]. A function f : [0, 1] → R is said to be a weighting function if f is non-negative, monoton increasing and satisfies the following normalization condition ∫ 1