Fuzzy interval cooperative games
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TL;DR
The F-core generalizes the interval core introduced by Alparslan, Branzei and Tijs in 2008 for games where the worth of any coalition is a compact interval of the real line and it is proved that this condition is necessary but not sufficient to guarantee the F- core to be non-empty.
Abstract
We introduce a core-like concept (called F-core) for games in which the worth of any coalition is given by means of a fuzzy interval. Such a class of cooperative games was introduced by Mares in 1999. Different from Mares' approach, the F-core generalizes the interval core introduced by Alparslan, Branzei and Tijs in 2008 for games where the worth of any coalition is a compact interval of the real line. Moreover, we introduce a balanced-like condition and prove that this condition is necessary but not sufficient to guarantee the F-core to be non-empty.