Naitoh, Takeshi; Nakayama, Akira Structures of sublattices related to Veinott relation. (English) Zbl 0883.90134 J. Oper. Res. Soc. Japan 40, No. 2, 276-280 (1997). Summary: Let \(E\) be a nonempty finite set. H. Narayanan showed a theorem describing that the family \(\left\{\Pi'\mid\Pi'\in P_E, \sum_{X\in\Pi'} f(X)= \min_{\Pi\in P_E} \sum_{X\in\Pi'} f(X)\right\}\) forms a lattice, where \(f\) is a submodular function on \(2^E\) and \(P_E\) is the set of all partitions of \(E\). On the other hand, L. S. Shapley gave a theorem on a necessary and sufficient condition for a convex game to be decomposable. We give a theorem which is a generalization of these two theorems. MSC: 91A12 Cooperative games 06B99 Lattices Keywords:Veinott relation; lattice; submodular function; convex game; decomposable PDFBibTeX XMLCite \textit{T. Naitoh} and \textit{A. Nakayama}, J. Oper. Res. Soc. Japan 40, No. 2, 276--280 (1997; Zbl 0883.90134) Full Text: DOI Link