A note on the core: Minimal conversely consistent enlargement

The Moulin reduction is extended by reducing the number of the players to the framework of fuzzy games. Based on this extended Moulin reduction, the axiomatic result of the core in Tadenuma’s case does not hold in the context of fuzzy games, and the core also violates the converse consistency. Therefore, we propose the minimal core, which possesses the converse consistency and is also the smallest solution satisfying the core.