MAXIMUM WEIGHTED INDEPENDENT SET WITH UNCERTAIN WEIGHTS

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.