Quadratic Programming Models and Method for Interval-Valued Cooperative Games with Fuzzy Coalitions
The purpose of this paper is to develop a quadratic programming method for solving interval-valued cooperative games with fuzzy coalitions. In this method, the interval-valued cooperative games with fuzzy coalitions are converted into the interval-valued cooperative games (with crisp coalitions) by using the Choquet integral. Two auxiliary quadratic programming models for solving the interval-valued cooperative games are constructed by using the least square method and distance between intervals. The proposed models and method are validated and compared with other similar methods. A numerical example is examined to demonstrate the validity, superiority and applicability of the method proposed in this paper.
Keywords and phrasesCooperative game Quadratic programming Dissatisfaction function Lagrange multiplier method Choquet integral Fuzzy coalition
This research was supported by the Soft Science Research Program of Fujian Province of China (No. 2016R0012), the Social Science Planning Program of Fujian Province of China (No. 2013C024), the Key Program of National Natural Science Foundation of China (No. 71231003), the National Natural Science Foundation of China (No. 71572040), the National Social Science Foundation of China (No. 13BGL150) and the Science and Technology Program of the Education Department of Fujian Province of China (No. JA13122).
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