Fuzzy Robust Convex Optimization with Linear Membership Functions and Its Applications

In this article, we derive a new kind of uncertain optimization problem by incorporating fuzziness into robust optimization and thus obtain the so-called fuzzy robust optimization model. For the proposed fuzzy robust optimization model, we derive its deterministically equivalent form (which is just a traditional optimization problem) for the case that constraints are linear in the uncertainty parameters. We successively apply the proposed model to reformulate the water resource allocation problem in Zhangye, Gansu and solve it numerically.