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July  2021, 8(3): 267-275. 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  July 2021 Early access  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 and Games, 2021, 8 (3) : 267-275. 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.

[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.

[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.

[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.

[5]

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

[6]

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

[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.

[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.

[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.

[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.

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

[13]

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

[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.

[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.

[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.

[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.

[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.

[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.

[20]

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

[21]

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

[22]

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

[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.

[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.

[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.

[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. 

[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.

[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.

[29]

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

[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.

[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. 

[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. 

[33]

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

show all references

References:
[1]

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

[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.

[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.

[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.

[5]

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

[6]

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

[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.

[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.

[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.

[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.

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

[13]

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

[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.

[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.

[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.

[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.

[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.

[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.

[20]

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

[21]

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

[22]

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

[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.

[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.

[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.

[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. 

[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.

[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.

[29]

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

[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.

[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. 

[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. 

[33]

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

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