(eng): The theory of cooperative games with vague cooperation is based on modelling fuzzy coalitions as fuzzy subsets of the set of all players who participate in the coalitions with some part of their /power/. Here, we suggest an alternative approach assuming that coalitions are formed by relatively compact groups of individual players each of which represents a specific common interest. Each individual player may participate in several such groups and, as their member, in several coalitions. Our aim is to show that such an alternative model of fuzzy coalitions, in spite of its seemingly higher complexity, others an interesting more sophisticated reaction of the structure of vague cooperation and of relations being in its background.