Airport Situations and Games with Grey Uncertainty

Airport situations have much attention in recent years. Here, we focus on an appealing rule introduced by the economists Baker-Thompson called the Baker-Thompson rule which provides a fair and easy share for the costs of the landings. On the other hand, uncertainty is a daily presence in real life. It affects our decision-making and may have influence on cooperation. Recently, various economic and Operations Research situations under uncertainty are studied. In this paper, we deal with airport situations, where the costs of the pieces of the runway are given by grey numbers. In this context, we expand the Baker- Thompson rule as a solution concept. Some properties regarding an allocation problem of an airport situation under uncertainty is considered and grey solutions are proposed. We introduce grey Baker-Thompson rule. Further, we give the axiomatic characterization of the grey Baker-Thompson rule by using the major and the minor axioms where we give the first characterization by using 𝒢IES, the second characterization is given by using 𝒢CUR and the third characterization is given by using 𝒢CLAST. Finally, we give an example to compare the grey solutions and grey Baker-Thompson rule.