A Further Discussion on Cores for Interval-Valued Cooperative Game

  • Xuan Zhao
  • Qiang Zhang
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 214)


In this paper, we give a further discussion on the core solution for cooperative games with fuzzy payoffs. Some notions and results from classical games are extended to fuzzy cooperative games. Using an example, we point out that the theorem about the nonempty of \(I\)-core proposed in 2008 was not sufficient. Furthermore, the equivalence relation between balanced game and nonempty core, which plays an important role in classic games, does not exist in interval-valued cooperative games. After all, the nonempty of \(I\)-core is proved under the convex situation. It perfects the theory of fuzzy core for interval-valued cooperative game.


Cooperative game Interval-valued Core Balanced game 



This work was supported by the National Natural Science Foundation of China and Specialized Research Fund for the Doctoral Program of Higher Education (No. 70771010, 71071018, 70801064, 20111101110036).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Management and EconomicsBeijing Institute of TechnologyBeijingChina

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