The λ-mean squared dispersion associated with a fuzzy random variable

In this paper we introduce a parameterized real-valued measure of the mean dispersion of a fuzzy random variable with respect to an arbitrary fuzzy number. This measure extends the second moment of a classical random variable, and is based on a parameterized distance between fuzzy numbers. Properties of the measure presented are analyzed, and the extension of the variance of a classical random variable, which particularizes the mean squared dispersion, is also examined. Some examples illustrating the computation and possible applications of the measure are included. Finally, a brief discussion about the interest of using a parameterized distance, and about some future directions of this study, is developed.