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Minimum-Risk Criteria in Two-Stage Fuzzy Random Programming

Based on mean chance theory, this paper presents a new class of two-stage fuzzy random minimum risk problem (FRMRP), and discusses its deterministic equivalent programming problem. Because the FRMRPs include fuzzy random variable parameters with infinite supports, they are inherently infinite-dimensional optimization problems that can rarely be solved directly. Therefore, an approximation approach to the original two-stage FRMRPs is proposed, which results in finite-dimensional approximating two-stage FRMRPs. After that, the paper deals with the convergence of the objective value of the approximating two-stage FRMRP to that of the original two-stage FRMRP.