Some properties of a new metric on the space of fuzzy numbers (Q1885735)

The paper discusses some properties of a new metric (called \(``\)the Hausdorff-Skorokhod metric\("\)) which was previously introduced by \textit{S. Y. Joo} and \textit{Y. K. Kim} [J. Math. Anal. Appl. 246, 576--590 (2000; Zbl 0986.54012)] on the space of fuzzy numbers in the Euclidean space \(\mathbb{R}^k\). It is proved that convergence in the Hausdorff-Skorokhod metric implies convergence in the sendograph metric, and that the Hausdorff-Skorokhod metric is not absolutely homogeneous and not translation invariant. The continuity of operations and convexity on the space of fuzzy numbers equipped with the Hausdorff-Skorokhod metric are also investigated.