Sampling Method for Robust Fuzzy Optimization

In this article, we derive a new kind of uncertain optimization problem by incorporating fuzziness into the current hot research topic robust optimization and thus obtain the so-called robust fuzzy optimization model. For the proposed robust fuzzy optimization model, we first derive its deterministically equivalent form(which is just a nonlinear optimization problem), and then analyze the property of the feasible set of it. We successively pose a sampling method for robust fuzzy convex optimization, with the sampled problem being polynomially solvable. The probability of feasibility of the sampling method is analyzed and the required sampling size to obtain this probability is also derived.