The Interval-Valued Least Square Solutions of Interval-Valued Cooperative Games

  • Deng-Feng Li


The aim of this chapter is to propose the concept of the interval-valued least square solution of interval-valued cooperative games and develop fast and effective quadratic programming methods for computing such interval-valued least square solutions. In this chapter, after briefly reviewing concepts of solutions of cooperative games and intervals as well as interval operations, based on the least square method and distance measure between intervals, we construct two quadratic programming models and obtain their analytical solutions, which are used to determine players’ interval-valued imputations. Hereby the interval-valued least square solutions of interval-valued cooperative games are determined in the sense of minimizing the loss functions. The quadratic programming models and method proposed in this chapter are compared with other methods to show the validity, the applicability, and the advantages.


Interval-valued cooperative game Least square method Loss function Mathematical programming Interval computation 


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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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