maximum weighted independent set with uncertain weights

The uncertainty theory from the viewpoint of liu is a new way to deal with problems which some of parameters are not deter- minate. especially, this theory is based on experts belifes and by in- troducing a measure in these belifes tries to overcome to uncertainty. maximum weighted independent set problem is a classic combinatorial optimization problem and has wide range of application such as schedul- ing. it is proved that this is an np-hrad problem and for arbitary graph, there are only approximate algorithms. in this paper, we investigate this problem with indeterministic weights and obtain an equivalant deminis- tic integer programming model. considering the concept of uncertainty distribution of an uncertain variable, one models is constructed based on -chance method.