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doi: 10.3934/jdg.2021010

On cooperative fuzzy bubbly games

Süleyman Demirel University, Faculty of Arts and Sciences, Department of Mathematics, Isparta, 32260, Turkey

* Corresponding author: ismailozcanmath@gmail.com

Received  July 2020 Revised  January 2021 Published  March 2021

The allocation problem of rewards/costs is a basic question for players namely individuals and companies that planning cooperation under uncertainty. The involvement of uncertainty in cooperative game theory is motivated by the real world where noise in observation and experimental design, incomplete information and further vagueness in preference structures and decision-making play an important role. In this paper we extend cooperative bubbly games to cooperative fuzzy bubbly games, where the worth of each coalition is a fuzzy bubble instead of an interval. Further, we introduce a set-valued concept called the fuzzy bubbly core. Finally, some results on fuzzy bubbly core are given.

Citation: İsmail Özcan, Sirma Zeynep Alparslan Gök. On cooperative fuzzy bubbly games. Journal of Dynamics & Games, doi: 10.3934/jdg.2021010
References:
[1]

S. Z. Alparslan Gök, Cooperative Interval Games, PhD Dissertation Thesis, Institute of Applied Mathematics, Middle East Technical University, 2009. Google Scholar

[2]

S. Z. Alparslan Gök, R. Branzei and S. Tijs, Convex interval games, J. Appl. Math. Decis. Sci, 2009 (2009), 342089, 14 pp. doi: 10.1155/2009/342089.  Google Scholar

[3]

S. Z Alparslan GökS. Miquel and S. Tijs, Cooperation under interval uncertainty, Mathematical Methods of Operations Research, 69 (2009), 99-109.  doi: 10.1007/s00186-008-0211-3.  Google Scholar

[4]

S. Z. Alparslan GökO. BranzeiR. Branzei and S. Tijs, Set-valued solution concepts using interval-type payoffs for interval games, Journal of Mathematical Economics, 47 (2011), 621-626.  doi: 10.1016/j.jmateco.2011.08.008.  Google Scholar

[5]

J. P. Aubin, Coeur et valeur des jeux flous àpaiements latéraux, C.R. Acad. Sci. Paris, 279 (1974), 891-894.   Google Scholar

[6]

J. P. Aubin, Cooperative fuzzy games, Mathematics of Operations Research, 6 (1981), 1-13.  doi: 10.1287/moor.6.1.1.  Google Scholar

[7]

A. BhaumikS. K. Roy and D. F. Li, Analysis of triangular intuitionistic fuzzy matrix games using robust ranking, Journal of Intelligent & Fuzzy Systems, 33 (2017), 327-336.  doi: 10.3233/JIFS-161631.  Google Scholar

[8]

R. BranzeiO. BranzeiS. Z. Alparslan Gök and and S. Tijs, Cooperative interval games: A survey, Central European Journal of Operations Research, 18 (2010), 397-411.  doi: 10.1007/s10100-009-0116-0.  Google Scholar

[9]

D. Butnariu, Fuzzy games: A description of the concept, Fuzzy Sets and Systems, 1 (1978), 181-192.  doi: 10.1016/0165-0114(78)90003-9.  Google Scholar

[10]

A. Charnes and D. Granot, Prior Solutions: Extensions of Convex Nucleus Solutions to Chance-Constrained Games, Texas Univ Austin Center For Cybernetic Studies, 1973. Google Scholar

[11] D. Dubois, Fuzzy Sets and Systems: Theory and Applications, Academic press, 1980.   Google Scholar
[12]

D. Dubois, E. Kerre, R. Mesiar and H. Prade, Fuzzy Interval Analysis, In Fundamentals of fuzzy sets, Springer, Boston, MA, 2000. doi: 10.1007/978-1-4615-4429-6_11.  Google Scholar

[13]

D. Granot, Cooperative games in stochastic characteristic function form, Management Science, 23 (1977), 621-630.  doi: 10.1287/mnsc.23.6.621.  Google Scholar

[14]

J. Jana and S. K. Roy, Dual hesitant fuzzy matrix games: Based on new similarity measure, Soft Computing, 23 (2019), 8873-8886.  doi: 10.1007/s00500-018-3486-1.  Google Scholar

[15]

W. Krabs and S. Pickl, A game-theoretic treatment of a time-discrete emission reduction model, International Game Theory Review, 6 (2004), 21-34.  doi: 10.1142/S0219198904000058.  Google Scholar

[16]

E. Kürüm, G. W. Weber and C. Iyigün, Financial bubbles, In: Modeling, Dynamics, Optimization and Bioeconomics I. Springer, Cham, (2014), 453-468. doi: 10.1007/978-3-319-04849-9_26.  Google Scholar

[17]

E. KürümG. W. Weber and C. Iyigün, Early warning on stock market bubbles via methods of optimization, clustering and inverse problems, Annals of Operations Research, 260 (2018), 293-320.  doi: 10.1007/s10479-017-2496-1.  Google Scholar

[18]

Y. F. LiS. Venkatesh and D. Li, Modeling global emissions and residues of pesticides, Environmental Modeling & Assessment, 9 (2005), 237-243.  doi: 10.1007/s10666-005-3151-9.  Google Scholar

[19]

L. MallozziV. Scalzo and S. Tijs, Fuzzy interval cooperative games, Fuzzy Sets and Systems, 165 (2011), 98-105.  doi: 10.1016/j.fss.2010.06.005.  Google Scholar

[20]

M. Mareš, Additivities in fuzzy coalition games with side-payments, Kybernetika, 35 (1999), 149-166.   Google Scholar

[21]

M. Mareš, Fuzzy Cooperative Games, Cooperation with Vague Expectations, Physica-Verlag, Heidelberg, 2001. doi: 10.1007/978-3-7908-1820-8.  Google Scholar

[22]

M. Mareš and M. Vlach, Fuzzy classes of cooperative games with transferable utility, Scientiae Mathematicae Japonica, 60 (2004), 269-278.   Google Scholar

[23]

I. Nishizaki and M. Sakawa, Fuzzy cooperative games arising from linear production programming problems with fuzzy parameters, Fuzzy Sets and Systems, 114 (2000), 11-21.  doi: 10.1016/S0165-0114(98)00134-1.  Google Scholar

[24]

O. PalancıS. Z. Alparslan Gök and G. W. Weber, Cooperative games under bubbly uncertainty, Mathematical Methods of Operations Research, 80 (2014), 129-137.  doi: 10.1007/s00186-014-0472-y.  Google Scholar

[25]

O. PalancıS. Z. Alparslan GökS. Ergün and G. W. Weber, Cooperative grey games and the grey Shapley value, Optimization, 64 (2015), 1657-1668.  doi: 10.1080/02331934.2014.956743.  Google Scholar

[26]

S. Pickl and G. W. Weber, Optimization of a time-discrete nonlinear dynamical system from a problem of ecology-an analytical and numerical approach, Journal of Computational Technologies, 6 (2001), 43-51.   Google Scholar

[27]

S. K. Roy and A. Bhaumik, Intelligent water management: A triangular type-2 intuitionistic fuzzy matrix games approach, Water Resources Management, 32 (2018), 949-968.  doi: 10.1007/s11269-017-1848-6.  Google Scholar

[28]

J. SuijsP. BormA. De Waegenaere and S. Tijs, Cooperative games with stochastic payoffs, European Journal of Operational Research, 113 (1999), 193-205.  doi: 10.1016/S0377-2217(97)00421-9.  Google Scholar

[29]

J. Timmer, P. Borm and S. Tijs, Convexity in Stochastic Cooperative Situations, Tilburg University, 2000. Google Scholar

[30]

G. W. Weber, R. Branzei and S. Z. Alparslan Gök, On cooperative ellipsoidal games, In 24th Mini EURO Conference-On Continuous Optimization and Information-Based Technologies in the Financial Sector, MEC EurOPT, (2010), 369-372. Google Scholar

[31]

G. W. WeberE. KropatA. Tezel and S. Belen, Optimization applied on regulatory and eco-finance networks - survey and new developments, In Pac. J. Optim, 6 (2010), 319-340.   Google Scholar

[32]

G. W. WeberP. TaylanK. Yıldırak and Z. K. Görg ülü, Financial regression and organization, Special Issue on Optimization in Finance, DCDIS-B, 17 (2010), 149-174.   Google Scholar

[33]

L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.  doi: 10.1016/S0019-9958(65)90241-X.  Google Scholar

show all references

References:
[1]

S. Z. Alparslan Gök, Cooperative Interval Games, PhD Dissertation Thesis, Institute of Applied Mathematics, Middle East Technical University, 2009. Google Scholar

[2]

S. Z. Alparslan Gök, R. Branzei and S. Tijs, Convex interval games, J. Appl. Math. Decis. Sci, 2009 (2009), 342089, 14 pp. doi: 10.1155/2009/342089.  Google Scholar

[3]

S. Z Alparslan GökS. Miquel and S. Tijs, Cooperation under interval uncertainty, Mathematical Methods of Operations Research, 69 (2009), 99-109.  doi: 10.1007/s00186-008-0211-3.  Google Scholar

[4]

S. Z. Alparslan GökO. BranzeiR. Branzei and S. Tijs, Set-valued solution concepts using interval-type payoffs for interval games, Journal of Mathematical Economics, 47 (2011), 621-626.  doi: 10.1016/j.jmateco.2011.08.008.  Google Scholar

[5]

J. P. Aubin, Coeur et valeur des jeux flous àpaiements latéraux, C.R. Acad. Sci. Paris, 279 (1974), 891-894.   Google Scholar

[6]

J. P. Aubin, Cooperative fuzzy games, Mathematics of Operations Research, 6 (1981), 1-13.  doi: 10.1287/moor.6.1.1.  Google Scholar

[7]

A. BhaumikS. K. Roy and D. F. Li, Analysis of triangular intuitionistic fuzzy matrix games using robust ranking, Journal of Intelligent & Fuzzy Systems, 33 (2017), 327-336.  doi: 10.3233/JIFS-161631.  Google Scholar

[8]

R. BranzeiO. BranzeiS. Z. Alparslan Gök and and S. Tijs, Cooperative interval games: A survey, Central European Journal of Operations Research, 18 (2010), 397-411.  doi: 10.1007/s10100-009-0116-0.  Google Scholar

[9]

D. Butnariu, Fuzzy games: A description of the concept, Fuzzy Sets and Systems, 1 (1978), 181-192.  doi: 10.1016/0165-0114(78)90003-9.  Google Scholar

[10]

A. Charnes and D. Granot, Prior Solutions: Extensions of Convex Nucleus Solutions to Chance-Constrained Games, Texas Univ Austin Center For Cybernetic Studies, 1973. Google Scholar

[11] D. Dubois, Fuzzy Sets and Systems: Theory and Applications, Academic press, 1980.   Google Scholar
[12]

D. Dubois, E. Kerre, R. Mesiar and H. Prade, Fuzzy Interval Analysis, In Fundamentals of fuzzy sets, Springer, Boston, MA, 2000. doi: 10.1007/978-1-4615-4429-6_11.  Google Scholar

[13]

D. Granot, Cooperative games in stochastic characteristic function form, Management Science, 23 (1977), 621-630.  doi: 10.1287/mnsc.23.6.621.  Google Scholar

[14]

J. Jana and S. K. Roy, Dual hesitant fuzzy matrix games: Based on new similarity measure, Soft Computing, 23 (2019), 8873-8886.  doi: 10.1007/s00500-018-3486-1.  Google Scholar

[15]

W. Krabs and S. Pickl, A game-theoretic treatment of a time-discrete emission reduction model, International Game Theory Review, 6 (2004), 21-34.  doi: 10.1142/S0219198904000058.  Google Scholar

[16]

E. Kürüm, G. W. Weber and C. Iyigün, Financial bubbles, In: Modeling, Dynamics, Optimization and Bioeconomics I. Springer, Cham, (2014), 453-468. doi: 10.1007/978-3-319-04849-9_26.  Google Scholar

[17]

E. KürümG. W. Weber and C. Iyigün, Early warning on stock market bubbles via methods of optimization, clustering and inverse problems, Annals of Operations Research, 260 (2018), 293-320.  doi: 10.1007/s10479-017-2496-1.  Google Scholar

[18]

Y. F. LiS. Venkatesh and D. Li, Modeling global emissions and residues of pesticides, Environmental Modeling & Assessment, 9 (2005), 237-243.  doi: 10.1007/s10666-005-3151-9.  Google Scholar

[19]

L. MallozziV. Scalzo and S. Tijs, Fuzzy interval cooperative games, Fuzzy Sets and Systems, 165 (2011), 98-105.  doi: 10.1016/j.fss.2010.06.005.  Google Scholar

[20]

M. Mareš, Additivities in fuzzy coalition games with side-payments, Kybernetika, 35 (1999), 149-166.   Google Scholar

[21]

M. Mareš, Fuzzy Cooperative Games, Cooperation with Vague Expectations, Physica-Verlag, Heidelberg, 2001. doi: 10.1007/978-3-7908-1820-8.  Google Scholar

[22]

M. Mareš and M. Vlach, Fuzzy classes of cooperative games with transferable utility, Scientiae Mathematicae Japonica, 60 (2004), 269-278.   Google Scholar

[23]

I. Nishizaki and M. Sakawa, Fuzzy cooperative games arising from linear production programming problems with fuzzy parameters, Fuzzy Sets and Systems, 114 (2000), 11-21.  doi: 10.1016/S0165-0114(98)00134-1.  Google Scholar

[24]

O. PalancıS. Z. Alparslan Gök and G. W. Weber, Cooperative games under bubbly uncertainty, Mathematical Methods of Operations Research, 80 (2014), 129-137.  doi: 10.1007/s00186-014-0472-y.  Google Scholar

[25]

O. PalancıS. Z. Alparslan GökS. Ergün and G. W. Weber, Cooperative grey games and the grey Shapley value, Optimization, 64 (2015), 1657-1668.  doi: 10.1080/02331934.2014.956743.  Google Scholar

[26]

S. Pickl and G. W. Weber, Optimization of a time-discrete nonlinear dynamical system from a problem of ecology-an analytical and numerical approach, Journal of Computational Technologies, 6 (2001), 43-51.   Google Scholar

[27]

S. K. Roy and A. Bhaumik, Intelligent water management: A triangular type-2 intuitionistic fuzzy matrix games approach, Water Resources Management, 32 (2018), 949-968.  doi: 10.1007/s11269-017-1848-6.  Google Scholar

[28]

J. SuijsP. BormA. De Waegenaere and S. Tijs, Cooperative games with stochastic payoffs, European Journal of Operational Research, 113 (1999), 193-205.  doi: 10.1016/S0377-2217(97)00421-9.  Google Scholar

[29]

J. Timmer, P. Borm and S. Tijs, Convexity in Stochastic Cooperative Situations, Tilburg University, 2000. Google Scholar

[30]

G. W. Weber, R. Branzei and S. Z. Alparslan Gök, On cooperative ellipsoidal games, In 24th Mini EURO Conference-On Continuous Optimization and Information-Based Technologies in the Financial Sector, MEC EurOPT, (2010), 369-372. Google Scholar

[31]

G. W. WeberE. KropatA. Tezel and S. Belen, Optimization applied on regulatory and eco-finance networks - survey and new developments, In Pac. J. Optim, 6 (2010), 319-340.   Google Scholar

[32]

G. W. WeberP. TaylanK. Yıldırak and Z. K. Görg ülü, Financial regression and organization, Special Issue on Optimization in Finance, DCDIS-B, 17 (2010), 149-174.   Google Scholar

[33]

L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.  doi: 10.1016/S0019-9958(65)90241-X.  Google Scholar

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