A class of decentralized bi-level programming with multi-objectives in the upper level

In this paper, a class of decentralized bi-level programming model with multi-objectives in the upper level is introduced, in which discrete fuzzy random parameters are considered. To make the model calculable, we apply a transformation method to transform the discrete fuzzy random variables into fuzzy numbers which are then dealt with using an expected value method. As it is very difficult to solve bi-level model even if it is linear with single objective in each level, an interactive fuzzy programming with weighted sum method is applied to transform the bi-level to a single level model which is then solved using Lingo 13.0. Finally, the efficiency of the optimization method is verified using a numerical example.