On Sequencing Fuzzy Interval Games

• Autorzy: Özcan İsmail , Alparslan Gök Sırma Zeynep , Weber Gerhard-Wilhelm

Identyfikatory

DOI

10.24425/mper.2023.147199

• Języki publikacji: EN

Abstrakty

EN

In sequencing situations, it may affect parameters used to determine an optimal order in the queue, and consequently the decision of whether (or not) to rearrange the queue by sharing the realized cost savings. In this paper, we extend one machine sequencing situations and their related cooperative games under fuzzy uncertainty. Here, the agents costs per unit of time and processing time in the system are fuzzy intervals. In the sequel, we define sequencing fuzzy interval games and show that these games are convex. Further, fuzzy equal gain splitting rule is given. Finally, a numerical example is illustrated priority based scheduling algorithm.

Słowa kluczowe

EN

sequencing situations; fuzzy interval; cooperative game; convex game; equal gain splitting rule

• Wydawca: Production Engineering Committee of the Polish Academy of Sciences ; Polish Association for Production Management
• Czasopismo: Management and Production Engineering Review
• Rocznik: 2023
• Tom: Vol. 14, No. 4
• Strony: 10--18
• Opis fizyczny: Bibliogr. 34 poz., tab.

Twórcy

autor

Özcan İsmail

• Süleyman Demirel University, East Campus, Faculty of Arts and Sciences, Department of Mathematics, 32260 Çünür/Isparta, Turkey

autor

Alparslan Gök Sırma Zeynep

• Süleyman Demirel University, East Campus, Faculty of Arts and Sciences, Department of Mathematics, 32260 Çünür/Isparta, Turkey

autor

Weber Gerhard-Wilhelm

• Poznan University of Technology, Departments of Management Engineering, Poland

Bibliografia

• Alparslan Gök, S.Z., Branzei, R., & Tijs, S. (2009). Convex interval games. Advances in Decision Sciences, (2009a), Mathematical Methods of Operations Research, 69(1), 99-109.
• Alparslan Gök, S.Z., Branzei, O., Branzei, R., & Tijs, S. (2011), Set-valued solution concepts using intervaltype payoffs for interval games. Journal of Mathematical Economics, 47(4-5), 621-626, doi: 10.1016/j.jmateco.2011.08.008.
• Alparslan Gök, S.Z., Branzei, R., Fragnelli, V., & Tijs, S.H. (2008). Sequencing interval situations and related games, CEJOR, 21, 225-236, doi: 10.1007/s10100-011-0226-3.
• Alparslan Gök, S.Z., Miquel, S., & Tijs, S.H. (2009b), Cooperation under interval uncertainty, Mathematical Methods of Operations Research, 69(1), 99-109, doi: 1007/s00186-008-0211-3.
• Alparslan Gök, S.Z., & Özcan, I. (2023). On big boss fuzzy interval games, European Journal of Operational Research, 306(3), 1040-1046, doi: 10.1016/j.ejor.2022.03.026.
• Aubin J.P., (1974). Coeur et valeur des jeux flous àpaiements latéraux, C.R. Acad. Sci. Paris, 279 A, 891-894.
• Aubin, J.P. (1981). Cooperative fuzzy games, Mathematics of Operations Research, 6(1), 1–13, doi: 10.1287/moor.6.1.1.
• Branzei, R., Branzei, O., Gök, S.Z.A., & Tijs, S. (2010). Cooperative interval games: a survey, Central European Journal of Operations Research, 18(3), 397-411. doi: 10.1007/s10100-009-0116-0.
• Borm, P., Hamers, H., & Hendrickx, R. (2001). Operations research games: A survey, Top, 9(2), 139, doi: 10.1007/BF02579075.
• Butnariu, D. (1978). Fuzzy games: a description of the concept, Fuzzy Sets and Systems, 1(3), 181-192, doi: 10.1016/0165-0114(78)90003-9.
• Calleja P., Estevez Fernandez M.A., Borm P., & Hamers H., (2006). Job scheduling, cooperation, and control, Operations Research Letters, 34(1), 22-28, doi: 10.1016/j.orl.2005.01.007.
• Curiel, I., Pederzoli, G., & Tijs, S. (1989). Sequencing games, European Journal of Operational Research, 40(3), 344-351, doi: 10.1016/0377-2217(89)90427-X.
• Curiel, I., Hamers, H., & Klijn, F. (2002). Sequencing games: a survey, In Chapters in game theory (pp. 27-50). Springer, Boston, MA.
• Dubois, D.J. (1980). Fuzzy sets and systems: theory and applications (Vol. 144). Academic Press.
• Dubois, D., & Prade, H. (1997). The three semantics of fuzzy sets, Fuzzy Sets and Systems, 90(2), 141-150, doi: 10.1016/S0165-0114(97)00080-8.
• Dubois, D., Kerre, E., Mesiar, R., & Prade, H. (2000). Fuzzy interval analysis, In Fundamentals of fuzzy sets (pp. 483-581). Springer, Boston, MA, doi: 10.1007/978-1-4615-4429-6_11.
• Ergün, S., Palanci, O., Gök, S.Z.A., Nizamoğlu, Ş., & Weber, G.W. (2020). Sequencing grey games, Journal of Dynamics & Games, 7(1), 21, doi: 10.3934/jdg.2020002.
• Hamidoğlu, A., Taghiyev, M.H., & Weber, G.W. (2021). On building two-player games with treatment schedules for the SIR model, Azerbaijan J. Math., 11(2), 183-195.
• Hamidoğlu, A. (2021). A novel one target game model in the life insurance market, International Journal of Management Science and Engineering Management, 16(3), 221-228, doi: 10.1080/17509653.2021.1941370.
• Lawler, E.L., Lenstra, J.K., Kan, A.H.R., & Shmoys, D.B. (1993). Sequencing and scheduling: Algorithms and complexity, Handbooks in Operations Research and Management Science, 4, 445-522.
• Kong, Q., Sun, H., Xu, G., & Hou, D. (2018). The general prenucleolus of n-person cooperative fuzzy games, Fuzzy Sets and Systems, 349, 23-41, doi: 10.1016/j.fss.2017.08.005.
• Mallozzi, L., Scalzo, V., & Tijs, S. (2011). Fuzzy interval cooperative games. Fuzzy Sets and Systems, 165(1), 98-105, doi: 10.1016/j.fss.2010.06.005.
• Mareš, M. (1999). Additivities in fuzzy coalition games with side-payments. Kybernetika, 35(2), 149-166.
• Mareš M, (2001). Fuzzy Cooperative Games, PhysicaVerlag, Heidelberg, doi: 10.1007/978-3-7908-1820-8.
• Mareš, M., & Vlach, M. (2004). Fuzzy classes of cooperative games with transferable utility. Scientiae Mathematicae Japonica, 2, 269-278.
• Meng, F., Chen, X., & Tan, C. (2016). Cooperative fuzzy games with interval characteristic functions, Operational research, 16(1), 1-24, doi: 10.1007/s12351-015-0183-z.
• Özcan, İ., & Gök, S.Z.A. (2021a). On cooperative fuzzy bubbly games, Journal of Dynamics and Games, 8(3), 267–275, doi: 10.3934/jdg.2021010.
• Özcan, İ., & Gök, S.Z.A. (2021b). On the fuzzy interval equal surplus sharing solutions, Kybernetes, 51(9), 2753-2767. doi: 10.1108/K-09-2020-0554.
• Özcan, İ., Śledziński, J.D., Gök, S.Z.A., Butlewski, M., & Weber, G.W. (2022). Mathematical encouragement of companies to cooperate by using cooperative games with fuzzy approach, Journal of Industrial and Management Optimization 19(10), 7180-7195, doi: 10.3934/jimo.2022258.
• Özcan, İ., Gök, S.Z.A., & Weber, G.W. (2023). Peer group situations and games with fuzzy uncertainty, Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2023084.
• Savku, E., & Weber, G.W. (2020). Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market, Annals of Operations Research, 1-26. doi: 10.1007/s10479-020-03768-5.
• Smith, W.E. (1956). Various optimizers for single-stage production, Naval Research Logistics Quarterly, 3(1- 2), 59-66.
• Yu, X., and Zhang, Q. (2010). An extension of cooperative fuzzy games, Fuzzy Sets and Systems, 161(11), 1614-1634, doi: 10.1016/j.fss.2009.08.001.
• Zadeh, L.A. (1965). Fuzzy sets, Information and Control, 8(3), 338-353, doi: 10.1016/S0019-9958(65)90241-X.