Generalized Proportional Solutions to Games with Restricted Cooperation

In TU-cooperative game with restricted cooperation the values of characteristic function $v(S)$ are defined only for $S\in \mathcal{A}$, where $\mathcal{A}$ is a collection of some nonempty coalitions of players. If $\mathcal{A}$ is a set of all singletones, then a claim problem arises, thus we have a claim problem with coalition demands.
We examine several generalizations of the Proportional method for claim problems: the Proportional solution, the Weakly Proportional solution, the Proportional Nucleolus, and $g$-solutions that generalize the Weighted Entropy solution. We describe necessary and sufficient condition on $\mathcal{A}$ for inclusion the Proportional Nucleolus in the Weakly Proportional solution and necessary and sufficient condition on $\mathcal{A}$ for inclusion $g$-solution in the Weakly Proportional solution. The necessary and sufficient condition on $\mathcal{A}$ for coincidence $g$-solution and the Weakly Proportional solution and sufficient condition for coincidence all $g$-solutions and the Proportional Nucleolus are obtained.