Abstract
The paper presents a solution to the problem of cost allocation for a communication network in which the connection values between two nodes are defined by a fuzzy utility function. The utility function can refer to both existing communication nodes and new node proposals. For the allocation mechanism, the authors used the fuzzy Shapley value built on a complete coalition of all paths connecting the root of the tree with all nodes of the given network.
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Notes
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A broader look at the value of Shapley in such situations can be found, for example, in the work of Gladysz and Mercik (2018).
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References
Algaba, E., Fragnelli, V., Llorca, N., Sanchez-Soriano, J.: Labeled network allocation problems. an application to transport systems. Trans. Comput. Collect. Intell. (2019, forthcoming)
Dubois, D., Prade, H.: Algorithmes de plus courts Chemins pour traiter des donnes floues. RAIRO Recherche Operationnelle/Oper. Res. 12, 213–227 (1978)
Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988)
Forlicz, S., Mercik, J., Stach, I., Ramsey, D.: The shapley value for multigraphs. In: Nguyen, N., Pimenidis, E., Khan, Z., Trawiński, B. (eds.) Computational Collective Intelligence. Lecture Notes in Computer Science, vol. 11056. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98446-9_20
Gładysz, B., Mercik, J.: The shapley value in fuzzy simple cooperative games. In: Nguyen, N.T., Hoang, D.H., Hong, T.P., Pham, H., Trawiński, B. (eds.) ACIIDS 2018. LNCS (LNAI), vol. 10751, pp. 410–418. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75417-8_39
Gambarelli, G., Owen, G.: Indirect control of corporations, International. J. Game Theory 23, 287–302 (1994)
Littlechild, S.C., Owen, G.: A simple expression for the Shapley value in special case. Manag. Sci. 20(3), 370–372 (1973)
Mercik, J.: Classification of committees with vetoes and conditions for the stability of power indices. Neurocomputing 149, 1143–1148 (2015)
Mercik, J.: Formal a priori power analysis of elements of a communication graph. In: Nguyen, N.T., Trawiński, B., Fujita, H., Hong, T.-P. (eds.) ACIIDS 2016. LNCS (LNAI), vol. 9621, pp. 410–419. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49381-6_39
Owen, G.: Game Theory, 3rd edn. Academic Press, San Diego (1995)
Rosenthal, E.C.: Shortest path games. Eur. J. Oper. Res. 224, 132–140 (2013)
Shapley, L.S.: A value for n-person games. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games volume II. Annals of Mathematical Studies, vol. 28, pp. 307–317. Princeton University Press, Princeton (1953)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Acknowledgements
The research is partially supported by the Polish Ministry of Science and Higher Education for Faculty of Computer Science and Management, Wroclaw University of Science and Technology (No 0401/0193/18), by AGH University of Science and Technology funds (No. 16.16.200.396) and by WSB University in Wroclaw.
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Gładysz, B., Mercik, J., Stach, I. (2019). Fuzzy Shapley Value-Based Solution for Communication Network. In: Nguyen, N., Chbeir, R., Exposito, E., Aniorté, P., Trawiński, B. (eds) Computational Collective Intelligence. ICCCI 2019. Lecture Notes in Computer Science(), vol 11683. Springer, Cham. https://doi.org/10.1007/978-3-030-28377-3_44
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