Max-consistency, complement-consistency and the core of fuzzy games

Recently, Hwang introduced two extensions of the max-reduced game to fuzzy games by reducing the number of the players. Based on these reduced games, he offered analogous axiomatizations of the core related to Serrano and Volij in the context of fuzzy games. Here, we continue and develop Hwang's work on similar topics. However, we turn to a different definition of the reduced game by simultaneously reducing both the number of the players and the participation levels. We propose such extensions of the complement-reduced game and of the max-reduced game to fuzzy games and define the related properties of consistency and converse consistency. Based on these properties, we offer several analogous characterizations of the core related to Peleg, Serrano and Volij and Tadenuma, respectively.