Chance-constrained Methods for Optimization Problems with Random and Fuzzy Parameters

On the basis of the possibility measure, necessity measure, credibility measure and probability measure, chance-constrained programming models are designed to treat optimization problems with stochastic and fuzzy parameters. Then, mathematical properties of different models, for instance, crisp equivalents of uncertain functions and constraints, are discussed on condition that parameters are uniformly distributed random variables and trapezoidal fuzzy variables. To solve the models, a genetic algorithm based on the simulation is designed to seek the approximate optimal solution. Finally, numerical examples are given to show the performance of models and algorithm.