Geodesic
Cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions
Kybernetika, Tome 42 (2006) no. 4, pp. 461-473
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Cooperative games are very useful in considering profit allocation among multiple decision makers who cooperate with each other. In order to deal with cooperative games in practical situations, however, we have to deal with two additional factors. One is some restrictions on coalitions. This first factor has been taken into consideration through feasibility of coalitions. The other is partial cooperation of players. In order to describe this second factor, we consider fuzzy coalitions which permit partial participation in a coalition to a player. In this paper we take both of these factors into account in cooperative games. Namely, we analyze and discuss cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions in two approaches. For the purpose of comparison of these two approaches, we define two special classes of extensions called $U$-extensions which satisfy linearity and $W$-extensions which satisfy $U$-extensions and two additional conditions, restriction invariance and monotonicity. Finally, we show sufficient conditions under which these obtained games in two approaches coincide.
Cooperative games are very useful in considering profit allocation among multiple decision makers who cooperate with each other. In order to deal with cooperative games in practical situations, however, we have to deal with two additional factors. One is some restrictions on coalitions. This first factor has been taken into consideration through feasibility of coalitions. The other is partial cooperation of players. In order to describe this second factor, we consider fuzzy coalitions which permit partial participation in a coalition to a player. In this paper we take both of these factors into account in cooperative games. Namely, we analyze and discuss cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions in two approaches. For the purpose of comparison of these two approaches, we define two special classes of extensions called $U$-extensions which satisfy linearity and $W$-extensions which satisfy $U$-extensions and two additional conditions, restriction invariance and monotonicity. Finally, we show sufficient conditions under which these obtained games in two approaches coincide.
Classification : 91A12
Keywords: cooperative games; cooperative fuzzy games; restricted games; coalitions 
@article{KYB_2006_42_4_a5,
     author = {Moritani, Atsushi and Tanino, Tetsuzo and Tatsumi, Keiji},
     title = {Cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions},
     journal = {Kybernetika},
     pages = {461--473},
     year = {2006},
     volume = {42},
     number = {4},
     mrnumber = {2275348},
     zbl = {1249.91010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006_42_4_a5/}
}
TY  - JOUR
AU  - Moritani, Atsushi
AU  - Tanino, Tetsuzo
AU  - Tatsumi, Keiji
TI  - Cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions
JO  - Kybernetika
PY  - 2006
SP  - 461
EP  - 473
VL  - 42
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_2006_42_4_a5/
LA  - en
ID  - KYB_2006_42_4_a5
ER  - 
%0 Journal Article
%A Moritani, Atsushi
%A Tanino, Tetsuzo
%A Tatsumi, Keiji
%T Cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions
%J Kybernetika
%D 2006
%P 461-473
%V 42
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_2006_42_4_a5/
%G en
%F KYB_2006_42_4_a5
Moritani, Atsushi; Tanino, Tetsuzo; Tatsumi, Keiji. Cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions. Kybernetika, Tome 42 (2006) no. 4, pp. 461-473. http://geodesic.mathdoc.fr/item/KYB_2006_42_4_a5/

[1] Algaba E., Bilbao J. M., Lopez J.: A unified approach to restricted games. Theory and Decision 50 (2001), 333–345 | DOI | MR | Zbl

[2] Aubin J. P.: Mathematical Methods of Game and Economic Theory. North–Holland, Amsterdam 1979 | MR | Zbl

[3] Bilbao J. M.: Cooperative Games on Combinatorial Structures. Kluwer Academic Publishers, Boston 2000 | MR | Zbl

[4] Brânzei R.: Convex fuzzy games and partition monotonic allocation schema. Fuzzy Sets and Systems 139 (2003), 267–281 | MR

[5] Lovász L.: Submodular functions and convexity. In: Mathematical Programming: The State of the Art (A. Bachem et al., eds.), Springer–Verlag, Berlin 1983, pp. 235–257 | MR | Zbl

[6] Mareš M.: Fuzzy Cooperative Games. Physica–Verlag, Heidelberg 2001 | MR | Zbl

[7] Moritani A., Tanino T., Kuroki, K., Tatsumi K.: Cooperative fuzzy games with restrictions on coalitions. In: Proc. Third Internat. Conference on Nonlinear Analysis and Convex Analysis 2004, pp. 323–345 | MR | Zbl

[8] Nishizaki I., Sakawa M.: Fuzzy and Multiobjective Games for Conflict Resolution. Physical–Verlag, Heidelberg 2001 | MR | Zbl

[9] Owen G.: Multilinear extensions of games. Management Sci. 18 (1972), 64–79 | DOI | MR | Zbl

[10] Tanino T.: Cooperative fuzzy games as extensions of ordinary cooperative games. In: Proc. 7th Czech–Japan Seminar on Data Analysis and Decision Making under Uncertainty (H. Noguchi, H. Ishii, M. Inuiguchi, eds.), Awaji Yumebutai ICC 2004, pp. 26–31