Study on the grey social welfare function

Based on interval grey numbers, the grey social welfare function (GSWF) is proposed in a group decision-making environment in this article. We proved that the GSWF satisfies unrestricted domain, Pareto principle, independence of irrelevant alternatives and has no dictator of Arrow´s Impossibility Theorem for binary social choice rule. So the GSWF is reasonable and fair. Application of the new preference representation to a singing competition demonstrates that the GSWF is fair and applicable.