Cooperative Games with the Intuitionistic Fuzzy Coalitions and Intuitionistic Fuzzy Characteristic Functions
In this paper, the definition of the Shapley function for intuitionistic fuzzy cooperative games is given by extending the fuzzy cooperative games. Based on the extended Hukuhara difference, the specific expression of the Shapley intuitionistic fuzzy cooperative games with multilinear extension form is obtained, and its existence and uniqueness are discussed. Furthermore, the properties of the Shapley function are researched. Finally, the validity and applicability of the proposed method, as well as comparison analysis with other methods are illustrated with a numerical example.
KeywordsIntuitionistic fuzzy cooperative games Shapley function Multilinear extension
This research was sponsored by the National Natural Science Foundation of China (No.71231003), the National Natural Science Foundation of China (Nos. 71561008, 71461005), the Science Foundation of Guangxi Province in China (No. 2014GXNSFAA118010) and the Graduate Education Innovation Project Foundation of Guilin University of Electronic Technology (No. 2016YJCX0).
- 1.Li, D.F.: Fuzzy Multi objective Many-Person Decision Makings and Games. National Defense Industry Press, Beijing (2003)Google Scholar
- 3.Aubin, J.P.: Mathematical Methods of Game and Economic Theory. North-Holland, Amsterdam (1982)Google Scholar
- 5.Li, D.F.: Linear programming approach to solve interval-valued matrix games. Journal 39, 655–666 (2011)Google Scholar
- 6.Li, D.F.: Models and Methods for Interval-Valued Cooperative Games in Economic Management. Springer, Cham (2016)Google Scholar
- 8.Butnariu, D.: Fuzzy games: a description of the concept. Fuzzy Sets Syst. 1, 181–192 (1978)Google Scholar
- 18.Nishizaki, I., Sakawa, M.: Fuzzy and multiobjective games for conflict resolution. Stud. Fuzziness Soft Comput. 64(6) (2001)Google Scholar
- 21.Shapley, L.S.: A value for n-person of games. Ann. Oper. Res. 28, 307–318 (1953)Google Scholar
- 29.Li, D.F., Nan, J.X.: An extended weighted average method for MADM using intuitionistic fuzzy sets and sensitivity analysis. Crit. View 5, 5–25 (2011)Google Scholar
- 33.Li, D.F., Yang, J.: A difference-index based ranking bilinear programming approach to solving bi-matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers. J. Appl. Math. 2013(4), 1–10 (2013)Google Scholar
- 34.Mielcová, E.: Core of n-person transferable utility games with intuitionistic fuzzy expectations In: Jezic, G., Howlett, R., Jain, L. (eds.) Agent and Multi-Agent Systems: Technologies and Applications. Smart Innovation, Systems and Technologies, vol. 38. Springer, Cham (2015). doi 10.1007/978-3-319-19728-9_14
- 36.Mahapatra, G.S., Roy, T.K.: Intuitionistic fuzzy number and its arithmetic operation with application a system failure. J. Uncertain Syst. 7(2), 92–107 (2013)Google Scholar
- 37.Young, H.P.: Monotonic solutions of cooperative games. Int. J. Game Theory 14(2), 65–72 (1985)Google Scholar