Satisfactory Interval-Valued Cores of Interval-Valued Cooperative Games

  • Deng-Feng Li


The aim of this chapter is to develop an effective nonlinear programming method for computing interval-valued cores of interval-valued cooperative games. In this chapter, we define satisfactory degrees (or ranking indexes) of comparing intervals with the features of inclusion and/or overlap relations and discuss their important properties. Hereby we construct satisfactory crisp equivalent forms of interval-valued inequalities. Based on the concept of interval-valued cores, we derive the auxiliary nonlinear programming models for computing interval-valued cores of interval-valued cooperative games and propose corresponding bisection algorithm, which can always provide global optimal solutions. The developed models and method can provide cooperative chances under the situation of inclusion and/or overlap relations between interval-type coalitions’ values in which the Moore’s interval ranking method (or order relation between intervals) may not assure that an interval-valued core exists. The proposed method is a generalization of that based on the Moore’s interval ranking relation. The feasibility and applicability of the models and method proposed in this chapter are illustrated with a numerical example.


Interval-valued cooperative game Core Interval-valued core Interval ranking Mathematical programming Bisection method 


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Deng-Feng Li
    • 1
  1. 1.School of Economics and ManagementFuzhou UniversityFuzhouChina

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