IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v196y2009i1p234-245.html
   My bibliography  Save this article

A simplified expression of the Shapley function for fuzzy game

Author

Listed:
  • Li, Shujin
  • Zhang, Qiang

Abstract

In this paper, a simplified expression of the Shapley function for games with fuzzy coalition is proposed, which can be regarded as the generalization of Shapley functions defined in some particular games with fuzzy coalition. The simplified expression of the Shapley function is compared with two definitions established by Butnariu, Tsurumi et al. A conclusion is drawn that the simplified expression of the Shapley function is equivalent to Butnariu's definition when characteristic function is a game with proportional values, and is equivalent to Tsurumi's definition when characteristic function is a game with Choquet integral forms. Furthermore, from an angle of interaction between two participation levels, the properties of the two games defined by Butnariu and Tsurumi are respectively studied.

Suggested Citation

  • Li, Shujin & Zhang, Qiang, 2009. "A simplified expression of the Shapley function for fuzzy game," European Journal of Operational Research, Elsevier, vol. 196(1), pages 234-245, July.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:1:p:234-245
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00232-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tijs, S.H. & Brânzei, R. & Ishihara, S. & Muto, S., 2004. "On cores and stable sets for fuzzy games," Other publications TiSEM 66dd20be-cb4b-4b6d-937e-0, Tilburg University, School of Economics and Management.
    2. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 129(3), pages 596-618, March.
    3. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
    4. Butnariu, Dan & Kroupa, Tomas, 2008. "Shapley mappings and the cumulative value for n-person games with fuzzy coalitions," European Journal of Operational Research, Elsevier, vol. 186(1), pages 288-299, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. García-Martínez, Jose A. & Mayor-Serra, Antonio J. & Meca, Ana, 2020. "Efficient Effort Equilibrium in Cooperation with Pairwise Cost Reduction," MPRA Paper 105604, University Library of Munich, Germany.
    2. Armaghan Abed-Elmdoust & Reza Kerachian, 2012. "Water Resources Allocation Using a Cooperative Game with Fuzzy Payoffs and Fuzzy Coalitions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(13), pages 3961-3976, October.
    3. Tido Takeng, Rodrigue, 2022. "Uncertain production environment and communication structure," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    4. van den Brink, René & González-Arangüena, Enrique & Manuel, Conrado & del Pozo, Mónica, 2014. "Order monotonic solutions for generalized characteristic functions," European Journal of Operational Research, Elsevier, vol. 238(3), pages 786-796.
    5. Neog, Rupok & Borkotokey, Surajit, 2011. "Dynamic resource allocation in fuzzy coalitions : a game theoretic model," MPRA Paper 40074, University Library of Munich, Germany.
    6. Fanyong Meng & Qiang Zhang & Xiaohong Chen, 2017. "Fuzzy Multichoice Games with Fuzzy Characteristic Functions," Group Decision and Negotiation, Springer, vol. 26(3), pages 565-595, May.
    7. Li, Deng-Feng, 2012. "A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 223(2), pages 421-429.
    8. Surajit Borkotokey & Rupok Neog, 2012. "Allocating Profit Among Rational Players in a Fuzzy Coalition: A Game Theoretic Model," Group Decision and Negotiation, Springer, vol. 21(4), pages 439-459, July.
    9. Mojtaba Sadegh & Najmeh Mahjouri & Reza Kerachian, 2010. "Optimal Inter-Basin Water Allocation Using Crisp and Fuzzy Shapley Games," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(10), pages 2291-2310, August.
    10. Hsien-Chung Wu, 2019. "Cores and dominance cores of cooperative games endowed with fuzzy payoffs," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 219-257, June.
    11. Yu-Hsien Liao, 2017. "Fuzzy games: a complement-consistent solution, axiomatizations and dynamic approaches," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 257-268, September.
    12. Fanyong Meng & Xiaohong Chen & Chunqiao Tan, 2016. "Cooperative fuzzy games with interval characteristic functions," Operational Research, Springer, vol. 16(1), pages 1-24, April.
    13. Mojtaba Sadegh & Reza Kerachian, 2011. "Water Resources Allocation Using Solution Concepts of Fuzzy Cooperative Games: Fuzzy Least Core and Fuzzy Weak Least Core," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(10), pages 2543-2573, August.
    14. García-Martínez, Jose A. & Mayor-Serra, Antonio J. & Meca, Ana, 2023. "Efficient effort equilibrium in cooperation with pairwise cost reduction," Omega, Elsevier, vol. 121(C).
    15. Liu, Dehai & Ji, Xiaoxian & Tang, Jiafu & Li, Hongyi, 2020. "A fuzzy cooperative game theoretic approach for multinational water resource spatiotemporal allocation," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1025-1037.
    16. M. A. Hinojosa & S. Lozano & A. M. Mármol, 2018. "DEA production games with fuzzy output prices," Fuzzy Optimization and Decision Making, Springer, vol. 17(4), pages 401-419, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fanyong Meng & Qiang Zhang & Xiaohong Chen, 2017. "Fuzzy Multichoice Games with Fuzzy Characteristic Functions," Group Decision and Negotiation, Springer, vol. 26(3), pages 565-595, May.
    2. Fanyong Meng & Xiaohong Chen & Chunqiao Tan, 2016. "Cooperative fuzzy games with interval characteristic functions," Operational Research, Springer, vol. 16(1), pages 1-24, April.
    3. Zijun Li & Fanyong Meng, 2023. "The potential and consistency of the Owen value for fuzzy cooperative games with a coalition structure," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 387-414, September.
    4. Hsien-Chung Wu, 2019. "Cores and dominance cores of cooperative games endowed with fuzzy payoffs," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 219-257, June.
    5. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the shapley value: a new approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 153-167, February.
    6. Yu-Hsien Liao, 2017. "Fuzzy games: a complement-consistent solution, axiomatizations and dynamic approaches," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 257-268, September.
    7. Yaron Azrieli & Ehud Lehrer, 2007. "On some families of cooperative fuzzy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 1-15, September.
    8. Mojtaba Sadegh & Najmeh Mahjouri & Reza Kerachian, 2010. "Optimal Inter-Basin Water Allocation Using Crisp and Fuzzy Shapley Games," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(10), pages 2291-2310, August.
    9. Liu, Dehai & Ji, Xiaoxian & Tang, Jiafu & Li, Hongyi, 2020. "A fuzzy cooperative game theoretic approach for multinational water resource spatiotemporal allocation," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1025-1037.
    10. Tido Takeng, Rodrigue, 2022. "Uncertain production environment and communication structure," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    11. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    12. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Games, MDPI, vol. 8(4), pages 1-25, November.
    13. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Discussion Paper 2002-13, Tilburg University, Center for Economic Research.
    14. Xin Jiang & Yuyu Liu & Ranhang Zhao, 2019. "A Framework for Ecological Compensation Assessment: A Case Study in the Upper Hun River Basin, Northeast China," Sustainability, MDPI, vol. 11(4), pages 1-13, February.
    15. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2018. "An axiomatisation of the Banzhaf value and interaction index for multichoice games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381119, HAL.
    16. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    17. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2018. "On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application," European Journal of Operational Research, Elsevier, vol. 271(1), pages 120-140.
    18. Ulrich Faigle & Michel Grabisch, 2016. "Bases and linear transforms of TU-games and cooperation systems," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 875-892, November.
    19. Grabisch, Michel & Labreuche, Christophe & Vansnick, Jean-Claude, 2003. "On the extension of pseudo-Boolean functions for the aggregation of interacting criteria," European Journal of Operational Research, Elsevier, vol. 148(1), pages 28-47, July.
    20. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2019. "Interaction indices for multichoice games," Documents de travail du Centre d'Economie de la Sorbonne 19019, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:196:y:2009:i:1:p:234-245. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.