Possibilistic mean value and variance of fuzzy numbers: Some examples of application

In probability theory the expected value of functions of random variables plays a fundamental role in defining the basic characteristic measures of probability distributions. For example, the variance, covariance and correlation of random variables can be computed as the expected value of their appropriately chosen real valued functions. In possibility theory we can use the principle of expected value of functions on fuzzy sets to define variance, covariance and correlation of possibility distributions. Marginal probability distributions are determined from the joint one by the principle of ´falling integrals´ and marginal possibility distributions are determined from the joint possibility distribution by the principle of ´falling shadows´. In 2001 we introduced the notions of possibilistic mean value and variance of fuzzy numbers. In this paper we explain these notions from a pure probabilistic view and show some examples of their application from the literature.