A further discussion on fuzzy interval cooperative games

Abstract

The $\mathcal{F}$-core and the $\mathcal{F}$-balancedness have been introduced for fuzzy interval cooperative games by Mallozzi et al. (2011). It was pointed out that the $\mathcal{F}$-balancedness was a necessary but not sufficient condition for the non-emptiness of the $\mathcal{F}$-core. In this paper, a numerical example is given to show that the $\mathcal{F}$-balancedness can not guarantee the non-emptiness of the $\mathcal{F}$-core. Furthermore, the $\mathcal{F}$-cores of trapezoidal fuzzy interval games are discussed in detail. Some properties of the $\mathcal{F}$-core are obtained and three sufficient conditions for the non-emptiness of the $\mathcal{F}$-core are given. These conclusions are generalizations of the corresponding results in both interval cooperative game theory and classical cooperative game theory. Lastly, an application example is also provided.