مهدی جهانگیری

The uncertainty theory from the viewpoint of Liu is a new way to deal with problems which some of parameters are not determinate. Especially, this theory is based on experts belifes and by introducing a measure in these belifes tries to overcome to uncertainty. Maximum weighted stable set problem is a classic combinatorial optimization problem and has wide range of application such as scheduling. 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 deministic integer programming model. Considering the concept of uncertainty distribution of an uncertain variable, two different models are constructed. The first model considers α-chance method, and the second exploits the expected value of the uncertain variables. Both models are converted to deterministic ones.