Geodesic
A bi-average tree solution for probabilistic communication situations with fuzzy coalition
Kybernetika, Tome 55 (2019) no. 1, pp. 63-80
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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.
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.
DOI : 10.14736/kyb-2019-1-0063
Classification : 05C72, 91A12
Keywords: probabilistic communication situation; fuzzy coalition; average tree solution; maximal product spanning tree 
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Li, Xianghui; Sun, Hao; Hou, Dongshuang. A bi-average tree solution for probabilistic communication situations with fuzzy coalition. Kybernetika, Tome 55 (2019) no. 1, pp. 63-80. doi: 10.14736/kyb-2019-1-0063

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