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Abstract: 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. [Copyright &y& Elsevier]

Abstract: In the present paper, we concentrate on dealing with a class of multiobjective programming problems with random rough coefficients. We first discuss how to turn a constrained model with random rough variables into crisp equivalent models. Then an interactive algorithm which is similar to the interactive fuzzy satisfying method is introduced to obtain the decision maker’s satisfying solution. In addition, the technique of random rough simulation is applied to deal with general random rough objective functions and random rough constraints which are usually hard to convert into their crisp equivalents. Furthermore, combined with the techniques of random rough simulation, a genetic algorithm using the compromise approach is designed for solving a random rough multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms. [Copyright &y& Elsevier]