By considering supreme-utilities among fuzzy level (decision) vectors, we introduce an index and its efficient extension to investigate power mensuration mechanism in the framework of multicriteria fuzzy transferable-utility (TU) games. We also adopt reduced games and related consistency to analyze the rationality for these two indexes. Further, alternative formulation for the efficient index is also proposed by applying excess function. Based on reduced game and excess function, we introduce different dynamic processes for the efficient index.
AubinJ.P., Coeur et valeur des jeux flous á paiements latéraux,mie des Sciences, Comptes Rendus de l’Académie des Sciences279 (1974), 891–894.
2.
AubinJ.P., Cooperative fuzzy games, Mathematics of Operations Research6 (1981), 1–13.
3.
BanzhafJ.F., Weighted voting doesn’t work: A mathematical analysis, Rutgers Law Review19 (1965), 317–343.
4.
BorkotokeyS., MesiarR., The Shapley value of cooperative games under fuzzy settings: A survey, International Journal of General Systems43 (2014), 75–95.
5.
BrinkR., LannG., Axiomatizations of the normalized banzhaf value and the Shapley value, Social Choice and Welfare15 (1998), 567–582.
6.
ButnariuD., KroupaT., Shapley mappings and the cumulative value for n-person games with fuzzy coalitions, European Journal of Operational Research186 (2008), 288–299.
7.
ColemanJ.S., Control of collectivities and the power of a collectivity to act in: Social Choice, Gordon and Breach, LiebermanB., ed., London, UK, 1971, pp. 269–300.
8.
DubeyP., ShapleyL.S., Mathematical properties of the Banzhaf power index, Mathematics of Operations Research4 (1979), 99–131.
9.
GallegoI., FernándezJ.R., Jiménez-LosadaA., OrdóñezM., A Banzhaf value for games with fuzzy communication structure: Computing the power of the political groups in the European Parliament, Fuzzy sets and systems255 (2014), 128–145.
10.
HallerH., Collusion properties of values, International Journal of Game Theory23 (1994), 261–281.
11.
HwangY.A., Fuzzy games: A characterization of the core, Fuzzy Sets and Systems158 (2007), 2480–2493.
12.
LehrerE., An axiomatization of the Banzhaf value, International Journal of Game Theory17 (1998), 89–99.
13.
LiS., ZhangQ., A simplified expression of the Shapley function for fuzzy game, European Journal of Operational Research196 (2009), 234–245.
14.
MaschlerM., OwenG., The consistent Shapley value for hyperplane games, International Journal of Game Theory18 (1989), 389–407.
15.
MengF., ZhangQ., The Shapley value on a kind of cooperative fuzzy games, Journal of Computational Information Systems7 (2011), 1846–1854.
16.
MengF., ZhaoJ., ZhangQ., The Banzhaf value for fuzzy games with fuzzy payoffs, Information Technology Journal11 (2012), 262–268.
17.
MutoS., IshiharaS., FukudaS., TijsS., BranzeiR., Generalized cores and stable sets for fuzzy games, International Game Theory Review8 (2006), 95–109.
18.
OwenG., Multilinear extensions and the Banzhaf value, Naval Research Logistics Quart22 (1975), 741–750.
19.
OwenG., Characterization of the banzhaf-coleman index, SIAM Journal on Applied Mathematics35 (1978), 315–327.
20.
PelegB., On the reduced game property and its converse, International Journal of Game Theory15 (1986), 187–200.
21.
SerranoR., VolijO., Axiomatizations of neoclassical concepts for economies, Journal of Mathematical Economics30 (1998), 87–108.
22.
StearnsR.E., Convergent transfer schemes for n-person games, Trans Amer Math Soc134 (1968), 449–459.
23.
TadenumaK., Reduced games, consistency, and the core, International Journal of Game Theory20 (1992), 325–334.
24.
TanC., JiangZ.Z., ChenX., IpW.H., A Banzhaf function for a fuzzy game, IEEE Transactions on Fuzzy Systems22 (2014), 1489–1502.
25.
TijsS., BranzeiR., IshiharaS., MutoS., On cores and stable sets for fuzzy games, Fuzzy Sets and Systems146 (2004), 285–296.
