Abstract
In this paper, we define the concepts of interval-valued cores of interval-valued multiobjective n-person cooperative games and satisfactory degree (or ranking indexes) of comparing intervals with the features of inclusion and/or overlap relations. Hereby, the interval-valued cores can be computed by developing a new two-phase method based on the auxiliary nonlinear programming models. The proposed method can provide cooperative chances under the situations of inclusion and/or overlap relations between intervals in which the traditional interval ranking method may not always assure. The feasibility and applicability of the models and method proposed in this paper are illustrated with a numerical example.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bornstein, C.T., Maculan, N., Pascoal, M., Pinto, L.L.: Multiobjective combinatorial optimization problems with a cost and several bottleneck objective functions: an algorithm with reoptimization. Comput. Oper. Res. 39(9), 969–976 (2012)
Nishizaki, I., Sakawa, M.: Fuzzy and Multiobjective Games For Conflict Resolution. Physica Heidelberg, Boston (2001)
Tanino, T.: Multiobjective Cooperative Games with Restrictions on Coalitions Multiobjective Programming and Goal Programming: Theoretical Results and Practical Applications, pp. 167–174. Springer-Verlag, Heidelberg (2009). doi:10.1007/978-3-540-85646-7_16
Hu, B.Q., Wang, S.: A novel approach in uncertain programming - part II: a class of constrained nonlinear programming problems with interval objective functions. J. Ind. Manag. Optim. 2(4), 373–385 (2006)
Li, D.-F., Nan, J.-X., Zhang, M.-J.: Interval programming models for matrix games with interval payoffs. Optim. Methods Softw. 27(1), 1–16 (2012)
Li, D.-F.: Decision and Game Theory in Management with Intuitionistic Fuzzy Sets. Springer-Verlag, Heidelberg (2014). doi:10.1007/978-3-642-40712-3
Zhang, S.J., Wan, Z.: Polymorphic uncertain nonlinear programming model and algorithm for maximizing the fatigue life of v-belt drive. J. Ind. Manag. Optim. 8(2), 493–505 (2012)
Hu, C.Y., Kearfott, R.B., Korvin, A.D.: Knowledge Processing with Interval and Soft Computing, pp. 168–172. Springer Verlag, London (2008)
Ishihuchi, H., Tanaka, M.: Multiobjective programming in optimization of the interval objective function. Eur. J. Oper. Res. 48(2), 219–225 (1990)
Moore, R.: Methods and Applications of Interval Analysis. SIAM, Philadelphia (1979)
Nakahara, Y., Sasaki, M., Gen, M.: On the linear programming problems with interval coefficients. Int. J. Comput. Ind. Eng. 23(1–4), 301–304 (1992)
Senguta, A., Pal, T.K.: On comparing interval numbers. Eur. J. Oper. Res. 127(1), 28–43 (2000)
Branzei, R., Alparslan Gök, S.Z., Branzei, O.: Cooperative games under interval uncertainty: on the convexity of the interval undominated cores. CEJOR 19(4), 523–532 (2011)
Alparslan-Gök, S.Z., Branzei, R., Tijs, S.H.: Cores and stable sets for interval-valued games. Cent. Econ. Res. Tilburg Univ. 1, 1–14 (2008)
Liming, W., Qiang, Z.: A further discussion on fuzzy interval cooperative games. J. Intell. Fuzzy Syst. 31(1), 1–7 (2016)
Liming, W., Qiang, Z.: Sufficient conditions for the non-emptiness of the interval core. Oper. Res. Manag. Sci. 25(4), 1–4 (2016)
Sikorski, K.: Bisection is optimal. Numer. Math. 40, 111–117 (1982)
Acknowledgments
This research was sponsored by the National Natural Science Foundation of China (No.71231003, No.71171055), Social Science Planning Project of Fujian (No. FJ2015B185) and “Outstanding Young Scientific Research Personnel Cultivation Plan of Colleges and Universities in Fujian Province” as well as “Science and Technology Innovation Team of Colleges and Universities in Fujian Province”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Hong, FX., Li, DF. (2017). Two-Phase Nonlinear Programming Models and Method for Interval-Valued Multiobjective Cooperative Games. In: Li, DF., Yang, XG., Uetz, M., Xu, GJ. (eds) Game Theory and Applications. China GTA China-Dutch GTA 2016 2016. Communications in Computer and Information Science, vol 758. Springer, Singapore. https://doi.org/10.1007/978-981-10-6753-2_20
Download citation
DOI: https://doi.org/10.1007/978-981-10-6753-2_20
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6752-5
Online ISBN: 978-981-10-6753-2
eBook Packages: Computer ScienceComputer Science (R0)