Value of information and solution under VaR criterion for fuzzy random optimization problems

Under the Value-at-Risk (VaR) criterion, this paper studies on the value of information and solution for two-stage fuzzy random optimization problems. First, the value of perfect information (VPI) in VaR criterion is discussed by studying the difference of the wait-and-see (WS) solution and the here-and-now (HN) solution to the two-stage fuzzy random programming with VaR criterion. Then, the value of fuzzy random solution (VFRS) in VaR is examined by investigating the difference of the HN solution and the random solution (RS), as well as the difference of HN solution and the expected value (EV) solution. Finally, a lower bound and an upper bound for the HN solution are derived.