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.