Abstract
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.
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Li, DF. (2016). Satisfactory Interval-Valued Cores of Interval-Valued Cooperative Games. In: Models and Methods for Interval-Valued Cooperative Games in Economic Management. Springer, Cham. https://doi.org/10.1007/978-3-319-28998-4_2
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DOI: https://doi.org/10.1007/978-3-319-28998-4_2
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