Abstract
In this paper, a generalized form of fuzzy games with interval characteristic functions is proposed, which can be seen as an extension of games with crisp characteristic functions. Based on the extended Hukuhara difference, the interval Shapley function for interval fuzzy games is studied. Then, the concept of interval population monotonic allocation function (IPMAF) is defined. When interval fuzzy games are convex, we prove that the interval Shapley function is an IPMAF. Furthermore, two special types of interval fuzzy games are researched, and the associated interval Shapley function is studied.
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Acknowledgments
This work was supported by the State Key Program of National Natural Science of China (No. 71431006), the Funds for Creative Research Groups of China (No. 71221061), the Projects of Major International Cooperation NSFC (No. 71210003), the National Natural Science Foundation of China (Nos. 71201089, 71271217, 71201110 and 71271029), the National Science Foundation for Post-doctoral Scientists of China (2014M560655), and the Program for New Century Excellent Talents in University of China (No. NCET-12-0541).
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Meng, F., Chen, X. & Tan, C. Cooperative fuzzy games with interval characteristic functions. Oper Res Int J 16, 1–24 (2016). https://doi.org/10.1007/s12351-015-0183-z
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DOI: https://doi.org/10.1007/s12351-015-0183-z