Programming models-based method for deriving profits allocation scheme with interval-valued cooperative games

Abstract

Owing to the fact that the payoff of grand coalition is limited to players’ allocation, what is more, other players will not satisfy with the allocation scheme if one of the possible coalitions allocate too much. Based on this fact, it is better to pursuit the allocation scheme of all players in coalition are as close to the coalition’s payoff as possible. In contrast, if the allocation scheme of all players in coalition is far from the coalition’s payoff, this will lead to the instability of the coalition. To address this issue, several linear programming models are constructed for taking into account the players in the coalition with compromise limit constraints. First, the profits allocation model with undominated nonnegative excess vector is extended to interval-valued fuzzy environments. Second, several linear programming models are constructed respectively considering without and with coalitions’ compromise limit constraints. Third, an illustrative example in conjunction with comparative analyses is employed to demonstrate the validity and applicability of the proposed models. Finally, the relationship of the models is discussed between without and with coalitions’ compromise limit constraints.