Kybernetika 55 no. 1, 63-80, 2019

A bi-average tree solution for probabilistic communication situations with fuzzy coalition

Xianghui Li, Hao Sun and Dongshuang HouDOI: 10.14736/kyb-2019-1-0063


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.


fuzzy coalition, probabilistic communication situation, average tree solution, maximal product spanning tree


05C57, 05C72, 91A12


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