Fuzzy optimization problems with critical value-at-risk criteria

Based on value-at-risk (VaR) criteria, this paper presents a new class of two-stage fuzzy programming models. Because the fuzzy optimization problems often include fuzzy variables defined through continuous possibility distribution functions, they are inherently infinitedimensional optimization problems that can rarely be solved directly. Thus, algorithms to solve such optimization problems must rely on intelligent computing as well as approximating schemes, which result in approximating finite-dimenSiODal optimization problems. Motivated by this fact, we suggest an approximation method to evaluate critical VaR objective functions, and discuss the convergence of the approximation approach. Furthermore, we design a hybrid algorithm (HA) based on the approximation method, neural network (NN) and genetic algorithm (GA) to solve the proposed optimization problem, and provide a numerical example to test the effectiveness of the HA.