Affiliations: [a] Fujian Chuanzheng Communications College, Fuzhou, Fujian, China
| [b] College of Management, Fujian Agriculture and Forestry University, Fuzhou, Fujian, China
| [c] Business School, Sichuan University, Chengdu, Sichuan, China
| [d] School of Economics and Management, University of Electronic Science and Technology of China, Chengdu, Sichuan, China
Correspondence:
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Corresponding author. Jie Yang, College of Management, Fujian Agriculture and Forestry University, Fuzhou, Fujian, China. E-mail: [email protected]. and Deng-Feng Li, School of Economics and Management, University of Electronic Science and Technology of China, Chengdu, Sichuan, China. E-mail: [email protected].
Abstract: This paper proposes the concept of interval-valued average tree solution (“AT solution” for short) of graph cooperative games with interval-valued payoffs, and develop an effective and a direct simplified method for solving a subclass of interval-valued graph cooperative games. In this method, the interval-valued AT solution is proved to be a monotonic and non-decreasing function of coalitions’ values under specific condition. Hence, the lower and upper bounds of interval-valued AT solutions of graph cooperative games can be obtained directly by using the lower and upper bounds of the interval-valued coalitions’ payoffs, respectively. The proposed method gives better results than general interval subtraction and the partial subtraction operator methods. In addition, some important properties of the interval-valued AT solutions of interval-valued graph cooperative games are discussed. At last, the applicability and superiority of the proposed approach is demonstrated by comparing with other methods.
Keywords: Fuzzy game theory, interval-valued graph cooperative game, average tree
solution, restricted coalition, interval computing
