The variance formulas for triangular fuzzy random variables

Fuzzy random variable is a measurable mapping from a probability space to a collection of fuzzy variables. The variance is a fundamental concept for fuzzy random variables. Due to the difficulties involved in computing variance, we usually focus on searching for good approximation and simulation methods to solve a complex model. Based on the definition of the variance of a fuzzy random variable, this paper first presents precision formulas for the variances of triangular fuzzy random variables, which can be applied to fuzzy random optimization problems as we design algorithms to solve fuzzy random programming. Then, to apply the variance formulas, we provide two numerical examples.