Two-Phase Nonlinear Programming Models and Method for Interval-Valued Multiobjective Cooperative Games
In this paper, we define the concepts of interval-valued cores of interval-valued multiobjective n-person cooperative games and satisfactory degree (or ranking indexes) of comparing intervals with the features of inclusion and/or overlap relations. Hereby, the interval-valued cores can be computed by developing a new two-phase method based on the auxiliary nonlinear programming models. The proposed method can provide cooperative chances under the situations of inclusion and/or overlap relations between intervals in which the traditional interval ranking method may not always assure. The feasibility and applicability of the models and method proposed in this paper are illustrated with a numerical example.
KeywordsCooperative games Core Interval ranking Mathematical programming Satisfactory degree
This research was sponsored by the National Natural Science Foundation of China (No.71231003, No.71171055), Social Science Planning Project of Fujian (No. FJ2015B185) and “Outstanding Young Scientific Research Personnel Cultivation Plan of Colleges and Universities in Fujian Province” as well as “Science and Technology Innovation Team of Colleges and Universities in Fujian Province”.
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