Existence of an Aumann-Maschler fuzzy bargaining set and fuzzy kernels in TU fuzzy games

In this paper, we first give fuzzy extensions of the well-known solution concepts of kernel and prekernel for a transferable utility (TU) game and establish the existence of fuzzy kernels in TU fuzzy games which generalizes the corresponding result for classical TU games by Davis and Maschler [5]. We then prove that the fuzzy kernel is a subset of the fuzzy bargaining set in a TU fuzzy game, which gives the fuzzy counterpart of the corresponding fact for classical TU games by Davis and Maschler. As a consequence, we establish the existence of fuzzy Aumann-Maschler fuzzy bargaining sets for TU fuzzy games which generalizes the well-known existence theorem for bargaining sets by Aumann and Maschler [1] and Peleg [11].