Based on the supreme-utilities among fuzzy sets, we propose the supreme-consistent value. Further, we propose some equivalent relations to axiomatize the family of all fuzzy solutions that admit a potential. Based on these equivalent relations, two axiomatizations of the supreme-consistent value are proposed. By considering an extended reduced game, we also offer an axiomatization and a dynamic process of the supreme-consistent value respectively.
AubinJ.P., Coeur et valeur des jeux flous á paiements latéraux, Comptes Rendus de l’Académie des Sciences279 (1974), 891–894.
2.
AubinJ.P., Cooperative fuzzy games, Mathematics of Operations Research6 (1981), 1–13.
3.
BorkotokeyS. and MesiarR., The Shapley value of cooperative games under fuzzy settings: A survey, International Journal of General Systems43 (2014), 75–95.
4.
BranzeiR., DimitrovD. and TijsS., Convex fuzzy games and participation monotonic allocation schemes, Fuzzy Sets and Systems139 (2003), 267–281.
5.
BranzeiR., DimitrovD. and TijsS., Egalitarianism in convex fuzzy games, Mathematical Social Sciences47 (2004), 313–325.
6.
BranzeiR., DimitrovD. and TijsS., Hypercubes and compromise values for cooperative fuzzy games, Eupopean Journal of Operational Research155 (2004), 733–740.
7.
ButnariuD., Stability and Shapley value for an n-persons fuzzy game, Fuzzy Sets and Systems4 (1980), 63–72.
8.
ButnariuD. and KlementT., Triangular norm-based measures and games with fuzzy coalitions, Kluwer Academic Publishers, Dordrecht, 1993.
9.
CalvoE. and SantosJ.C., Potential in cooperative TU-games, Mathematical Social Sciences34 (1997), 175–190.
10.
HartS. and Mas-ColellA., Potential, value and consistency, Econometrica57 (1989), 589–614.
11.
HwangY.A., Fuzzy games: A characterization of the core, Fuzzy Sets and Systems158 (2007), 2480–2493.
12.
HwangY.A. and LiaoY.H., The consistent value of fuzzy games, Fuzzy Sets and Systems160 (2009), 644–656.
13.
LiS., ZhangQ., A simplified expression of the Shapley function for fuzzy game, Eupopean Journal of Operational Research196 (2009), 234–245.
14.
LiaoY.H., The Shapley value for fuzzy games: TU games approach, Economics Bulletin33 (2013), 192–197.
15.
MaschlerM. and OwenG., The consistent Shapley value for hyperplane games, International Journal of Game Theory18 (1989), 389–407.
16.
MengF. and ZhangQ., The Shapley value on a kind of cooperative fuzzy games, Journal of Computational Information Systems7 (2011), 1846–1854.
17.
MolinaE. and TejadaJ., The equalizer and the lexicographical solutions for cooperative fuzzy games: Characterizations and properties, Fuzzy Sets and Systems125 (2002), 369–387.
18.
MyersonR., Conference structures and fair allocation rules, International Journal of Game Theory9 (1980), 169–182.
19.
MutoS., IshiharaS., FukudaS., TijsS. and BranzeiR., Generalized cores and stable sets for fuzzy games, International Game Theory Review8 (2006), 95–109.
20.
OrtmannK.M., Preservation of differences, potential, conservity. Working paper 236. Inst. of Math. Ec., University of Bielefeld, 1995.
21.
OrtmannK.M., Conservation of energy in nonatomic games. Working paper 237. Inst. of Math. Ec., University of Bielefeld, 1995.
22.
SakawaM. and NishizakiI., A lexicographical concept in an n-person cooperative fuzzy games, Fuzzy Sets and Systems61 (1994), 265–275.
23.
ShapleyL.S., A value for n-person game, In: KuhnH.W. and TuckerA.W., (eds.), Contributions to the Theory of Games II, Princeton, 1953, pp. 307–317
24.
TijsS., BranzeiR., IshiharaS. and MutoS., On cores and stable sets for fuzzy games, Fuzzy Sets and Systems146 (2004), 285–296.
25.
TsurumiM., TaninoT. and InuiguchiM., A Shapley function on a class of cooperative fuzzy games, Eur J Oper Res129 (2001), 596–618.
