Generalizations of the concept of core of simple games and their characterization in terms of permission of voters

In this paper, we generalize the concept of core of simple games in two ways, and characterize them in terms of the permission of voters. The characterization gives us an insight about the alternatives in the core, the insight that is useful when we support the situations of group decision making. That is, if an alternative in the core is chosen as the final selection of a situation of group decision making, then no voter regrets the expression of his/her opinions in the interaction stage of the situation, and oppositely, if an alternative chosen as the final selection of the situation does not cause any regret for the expression of opinions to any voters, then the alternative belongs to the core.