Random fuzzy programming with chance measures defined by fuzzy integrals

A random fuzzy variable is a mapping from a possibility space to a collection of random variables. In random fuzzy decision systems, two kinds of scalar chance measures of random fuzzy event are presented by using fuzzy integrals, one is the equilibrium chance measure, the other is the mean chance measure. Also, the duality of both equilibrium chance and mean chance measures are discussed. Using the mean chance measure, a new class of random fuzzy programming is proposed. At the end of the paper, a hybrid intelligent algorithm is provided to solve three numerical examples. The results show that the algorithm is effective.