Geodesic
Superadditivity in general fuzzy coalition games
Kybernetika, Tome 36 (2000) no. 3, pp. 265-277 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The superadditivity and related concepts belong to the fundamental ones in the coalition game theory. Their definition in general coalition games (games without side-payments) is based on the set theoretical approaches. It means that in the case of fuzzy coalition games the set theoretical model can be modified into the fuzzy set theoretical one. In this paper, the coalition games without side-payments and with fuzzy expectations of the pay-offs of players are considered and it is shown that for such games the properties of superadditivity, subadditivity and additivity turn into fuzzy properties. Their relations to their deterministic counterparts are shown and some results regarding their formal structure are derived.
The superadditivity and related concepts belong to the fundamental ones in the coalition game theory. Their definition in general coalition games (games without side-payments) is based on the set theoretical approaches. It means that in the case of fuzzy coalition games the set theoretical model can be modified into the fuzzy set theoretical one. In this paper, the coalition games without side-payments and with fuzzy expectations of the pay-offs of players are considered and it is shown that for such games the properties of superadditivity, subadditivity and additivity turn into fuzzy properties. Their relations to their deterministic counterparts are shown and some results regarding their formal structure are derived.
Classification : 90C70, 91A12
Keywords: coalition game theory; fuzzy set 
@article{KYB_2000_36_3_a0,
     author = {Mare\v{s}, Milan},
     title = {Superadditivity in general fuzzy coalition games},
     journal = {Kybernetika},
     pages = {265--277},
     year = {2000},
     volume = {36},
     number = {3},
     mrnumber = {1773504},
     zbl = {1249.91008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2000_36_3_a0/}
}
TY  - JOUR
AU  - Mareš, Milan
TI  - Superadditivity in general fuzzy coalition games
JO  - Kybernetika
PY  - 2000
SP  - 265
EP  - 277
VL  - 36
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_2000_36_3_a0/
LA  - en
ID  - KYB_2000_36_3_a0
ER  - 
%0 Journal Article
%A Mareš, Milan
%T Superadditivity in general fuzzy coalition games
%J Kybernetika
%D 2000
%P 265-277
%V 36
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_2000_36_3_a0/
%G en
%F KYB_2000_36_3_a0
Mareš, Milan. Superadditivity in general fuzzy coalition games. Kybernetika, Tome 36 (2000) no. 3, pp. 265-277. http://geodesic.mathdoc.fr/item/KYB_2000_36_3_a0/

[1] Butnariu D., Klement E. P.: Triangular Norm–Based Measures and Games with Fuzzy Coalitions. Kluwer, Dordrecht 1993 | MR | Zbl

[2] Klir G. J., (eds.), Bo Yuan: Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems. Selected Papers by Lotfi A. Zadeh. World Scientific, Singapore – London – New Jersey 1996 | MR

[3] Mareš M.: Additivity in general coalition games. Kybernetika 14 (1978), 5, 350–368 | MR

[4] Mareš M.: Computation Over Fuzzy Quantities. CRC–Press, Boca Raton 1994 | MR | Zbl

[5] Mareš M.: Weak arithmetics of fuzzy numbers. Fuzzy Sets and Systems 91 (1997), 2, 143–154 | DOI | MR

[6] Mareš M.: Additivities in fuzzy coalition games with side–payments. Kybernetika 35 (1999), 2, 149–166 | MR

[7] Mareš M.: Superadditivity in fuzzy extensions of coalition games. Tatra Mountains Math. Journal 16 (1999), 6, 109–116 | MR | Zbl

[8] Mareš M.: Fuzzy coalitions structures. Fuzzy Sets and Systems, to appear

[9] Novák V.: Fuzzy Sets and Their Applications. A. Hilger, Bristol 1989 | MR | Zbl

[10] Rosenmüller J.: The Theory of Games and Markets. North–Holland, Amsterdam 1982 | Zbl

[11] Zadeh L. A.: Fuzzy sets. Inform. and Control 8 (1965), 3, 338–353 | DOI | MR | Zbl