An analog of Bondareva–Shapley theorem I. Non-emptiness of the core of fuzzy game

The paper deals with a generalization of the famous Bondareva–Shapley theorem on the core of TU cooperative game to the case of fuzzy blocking. The approach proposed is based on the concept of balanced collection of fuzzy coalitions. Introduced by the author, this extension of the classic notion of balanced collection of standard coalitions makes it possible to present a natural analog of balanced-ness for so-called fuzzy TU cooperative games. The main result of the paper states that similar to the standard games the new balanced-ness-like assumption is a necessary and sufficient condition for the non-emptiness of the core of fuzzy TU cooperative game.