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International Journal for Uncertainty Quantification
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ISSN Druckformat: 2152-5080
ISSN Online: 2152-5099

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International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2018021714
pages 527-542

A SIMPLIFIED METHOD FOR COMPUTING INTERVAL-VALUED EQUAL SURPLUS DIVISION VALUES OF INTERVAL-VALUED COOPERATIVE GAMES

Deng-Feng Li
School of Economics and Management, Fuzhou University, Fuzhou, Fujian 350108, China
Yin-Fang Ye
School of Economics and Management, Fuzhou University, Fuzhou, Fujian 350108, China

ABSTRAKT

Cooperative games with coalitions' values represented by intervals, which are often called interval-valued (IV) cooperative games, have currently become a hot research topic. For single-valued solutions of IV cooperative games, if the Moore's interval subtraction were used, then some unreasonable conclusions and issues result. This paper focuses on developing a simplified method without using the Moore's interval subtraction for solving the IV equal division values and IV equal surplus division values of IV cooperative games. In the methods, through defining some weaker coalition monotonicity-like conditions, it is proven that both equal division value and equal surplus division value of the defined associated cooperative game are monotonic and nondecreasing functions of the parameter α. Hence, the IV equal division values and IV equal surplus division values of IV cooperative games can be directly and explicitly obtained through determining their lower and upper bounds by using the lower and upper bounds of the IV coalitions' values, respectively. The method proposed in this paper uses coalition monotonicity-like conditions rather than the Moore's interval subtraction and hereby can effectively avoid the issues resulting from it. Moreover, some important properties of the IV equal division values and IV equal surplus division values of IV cooperative games are discussed. Finally, real numerical examples are used to demonstrate the feasibility and applicability of the methods proposed in this paper.


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