## Cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions.(English)Zbl 1249.91010

Summary: 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 which has been taken into consideration using feasibility of coalitions; the other is the 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, namely, we analyze and discuss cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions under two approaches. For the purpose of a 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, namely, restriction invariance and monotonicity. Finally, we show sufficient conditions under which the games obtained under these two approaches coincide.

### MSC:

 91A12 Cooperative games
Full Text:

### References:

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