Convergence of Optimal Solutions about Approximation Scheme for Fuzzy Programming with Minimum-Risk Criteria

Two-stage fuzzy minimum-risk problems (FMRPs) include fuzzy variable parameters defined through a possibility distribution, they are inherently infinite-dimensional optimization problems that can rarely be solved directly. Therefore, algorithms to solve such optimization problems must rely on intelligent computing as well as approximating scheme, which results in approximating finite-dimensional FMRPs. The purpose of this paper is to establish conditions under which the optimal objective value and optimal solution of such approximating two-stage FMRP converges to the optimal objective value and optimal solution of the original two-stage FMRP, respectively.