Some properties of a new metric on the space of fuzzy numbers
type: Item
instance of: scholarly article
title: Some properties of a new metric on the space of fuzzy numbers
zbMATH Open document ID: 1056.54007
DOI: 10.1016/S0165-0114(03)00281-1
author: Dae Sig Kim
author: Yun Kyong Kim
published in: Fuzzy Sets and Systems
publication date: 2004-11-12T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 2115165
zbMATH Keywords: Fuzzy numbers
zbMATH Keywords: The Hausdorff-Skorokhod metric
zbMATH Keywords: Translation invariance
zbMATH Keywords: Convex sets
MaRDI profile type: Publication
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full work available at URL: s0165-0114(03)00281-1
OpenAlex ID: W2071742716
description: scientific article; zbMATH DE number 2115165