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On Distances for Cooperative Games and Non-additive Measures with Communication Situations

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Rough Sets and Current Trends in Computing (RSCTC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8536))

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Abstract

Non-additive (fuzzy) measures also known as cooperative games or capacities are set functions that can be used to evaluate subsets of a reference set. In order to evaluate their similarities and differences, we can consider distances between pairs of measures.

Games have been extended to communication situations in which besides of the game there is a graph that establishes which sets are feasible (which coalitions are possible, which individuals can cooperate).

In this paper we consider the problem of defining a distance for pairs of measures when not all sets are feasible.

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References

  1. Abril, D., Navarro-Arribas, G., Torra, V.: Choquet Integral for Record Linkage. Annals of Operations Research 195, 97–110 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bilbao, J.M.: Cooperative Games on Combinatorial Structures. Kluwer Academic Publishers (2000)

    Google Scholar 

  3. Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1953)

    Article  MathSciNet  Google Scholar 

  4. De, A., Diakonikolas, I., Servedio, R.A.: The inverse Shapley value problem. Electronic Colloquium on Computational Complexity, Report No. 181 (2012)

    Google Scholar 

  5. Fujimoto, K.: Cooperative game as non-additive measure. In: Torra, V., Narukawa, Y., Sugeno, M. (eds.) Non-Additive Measures. Studies in Fuzziness and Soft Computing, vol. 310, pp. 131–171. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  6. Gallego, I., Fernández, J.R., Jiménez-Losada, A., Ordoñez, M.: A Banzhaf value for games with fuzzy communication structure: Computing the power of the political groups in the European Parliament. Fuzzy Sets and Systems (in press, 2014)

    Google Scholar 

  7. Jiménez-Losada, A., Fernández, J.R., Ordóñez, M.: Myerson values for games with fuzzy communication structure. Fuzzy sets and systems 213, 74–90 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kawabe, J.: Metrizability of the Lévy topology on the space of nonadditive measures on metric spaces. Fuzzy sets and systems 204, 93–105 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kajii, A., Kojima, H., Ui, T.: The Myerson Value for Complete Coalition Systems. Institute for Mathematical Sciences (IMS) preprint series # 2006-25 (previous version with title “A Refinement of the Myerson Value”) (2006)

    Google Scholar 

  10. Myerson, R.: Graphs and cooperation in games. Mathematics of Operations Research 2, 225–229 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  11. Sugeno, M.: Theory of Fuzzy Integrals and its Applications, Ph. D. Dissertation, Tokyo Institute of Technology, Tokyo, Japan (1974)

    Google Scholar 

  12. Torra, V., Narukawa, Y.: Modeling decisions: information fusion and aggregation operators. Springer (2007)

    Google Scholar 

  13. Torra, V., Narukawa, Y., Sugeno, M.: Carlson, On the f-divergence for non-additive measures (submitted)

    Google Scholar 

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Torra, V., Narukawa, Y. (2014). On Distances for Cooperative Games and Non-additive Measures with Communication Situations. In: Cornelis, C., Kryszkiewicz, M., Ślȩzak, D., Ruiz, E.M., Bello, R., Shang, L. (eds) Rough Sets and Current Trends in Computing. RSCTC 2014. Lecture Notes in Computer Science(), vol 8536. Springer, Cham. https://doi.org/10.1007/978-3-319-08644-6_27

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  • DOI: https://doi.org/10.1007/978-3-319-08644-6_27

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08643-9

  • Online ISBN: 978-3-319-08644-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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