Research On Stochastic Rough Programming Model Based On Synthesis Effect And Solution Mothed

In logistic distribution location, investment portfolio problem, industrial production problems and so on, there are many uncertain factors, and randomness and roughness as two kinds of uncertainty are widespread usually. How to deal with the uncertainty is important to get the decision making. In this paper, based on stochastic programming theory and rough set theory the solution models of stochastic programming, rough programming and stochastic rough programming are proposed, which solve the decision making problem with randomness and roughness.Firstly, by establishing a class of stochastic synthesis effect functions, the expectation, the variance and the distribution function of a random variable are considered together and the stochastic synthesis effect model is proposed, which is a crisp programming solution model. Secondly, the expectation, the variance and the trust function of a rough variable are considered together and the rough synthesis effect model is proposed, and the objective function and rough feasible are considered together, and the rough synthesis effect model based on rough feasible is proposed. They are crisp programming solution models. Thirdly, the expectation, the variance and the chance function of a random rough variable are considered together and the stochastic rough synthesis effect model is proposed, and the expectation, the variance of a random variable and feasible region based on covering similar relation are considered together and the stochastic rough synthesis effect model based on covering similar relation is proposed. They are crisp programming solution models.Based on the different decision making consciousness the different classes of synthesis effect function is given. The synthesis effect model can be shown to contain traditional solution models which are expectation value model, chance-constrained model and dependent-chance programming model by choosing different synthesis effect functions. It can be seen as a development of the traditional solution models. Because of the uncertain constraint in the synthesis effect model, the genetic algorithm with random simulation, rough simulation or random rough simulation is used to solve it in the solution procedure. Finally, numerical cases and illustrative examples are provided to show the effectiveness of the proposed method. It shows that with the proper synthesis effect functions the solutions of the synthesis effect model are better than other solution models.