Some properties of a new metric on the space of fuzzy numbers

This paper deals with some properties of a new metric (here called “the Hausdorff–Skorokhod metric”) previously introduced by Joo and Kim on the space of fuzzy numbers in the Euclidean space R^k. We first prove that convergence in the Hausdorff–Skorokhod metric implies convergence in the sendograph metric. Also, we show that the Hausdorff–Skorokhod metric is not absolutely homogeneous and not translation invariant, and investigate the continuity of operations and convexity on the space of fuzzy numbers equipped with the Hausdorff–Skorokhod metric.