A class of expected value multi-objective programming problems with random rough coefficients

The emphasis of this paper is to introduce two kinds of random rough variables. One is the discrete random rough variable, the other is the continuous random rough variable. The expected value model with random rough coefficients is proposed and some special models are discussed. In order to compute the expected value of some complicated functions, the technique of the random rough simulation is presented. Combined with genetic algorithm, it is applied to check the objective function and constraint function, and to obtain the optimal solution. Finally, some numerical examples are provided to show the effectiveness of the proposed technique.