Solution of nonlinear programming problem with interval grey parameters

We considered the nonlinear programming problems with interval grey number in the objective function when the distribution of grey number is known, and when it is unknown, according to historical data and related information of parameters, and combining with statistical knowledge, analyzed the solving method of that programming problem. When the probability distribution was known, we established the interval programming model for different instances whose objective function with grey numbers, and used the distribution information of data and historical information, adopted classic statistical method, Bayesian statistical method and minimized the posterior risk to estimate grey number, then transformed the interval programming model into a general programming model, and this solved the uncertain model.