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A bi-average tree solution for probabilistic communication situations with fuzzy coalition. (English) Zbl 1449.05187
Summary: A probabilistic communication structure considers the setting with communication restrictions in which each pair of players has a probability to communicate directly. In this paper, we consider a more general framework, called a probabilistic communication structure with fuzzy coalition, that allows any player to have a participation degree to cooperate within a coalition. A maximal product spanning tree, indicating a way of the greatest possibility to communicate among the players, is introduced, where the unique path from one player to another is optimal. We present a feasible procedure to find the maximal product spanning trees. Furthermore, for games under this model, a new solution concept in terms of the average tree solution is proposed and axiomatized by defining a restricted game in Choquet integral form.
MSC:
05C57 Games on graphs (graph-theoretic aspects)
05C72 Fractional graph theory, fuzzy graph theory
91A12 Cooperative games
05C76 Graph operations (line graphs, products, etc.)
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