On Epsilon-Cores of Cooperative Games with Fuzzy Payoffs

It is well known that, for cooperative games with transferable utility (and with crisp payoffs), the set of reasonable imputations is nonempty. It is also known for what values of $\varepsilon$ the set of reasonable imputations belongs to the $\varepsilon$-core. Then the $\varepsilon$-core is also nonempty. This result is of considerable interest, because the 0-core of a cooperative game can be empty, but if the $\varepsilon$-core is nonempty in this case for some small $\varepsilon>0$, then there exist imputations such that the difference in the properties between them and the imputations from the 0-core is small. In this paper, these results are generalized to the case of games with fuzzy payoffs.