The least upper bound of content for realizable matrices on lattice \([0,1]\)
type: Item
instance of: scholarly article
title: The least upper bound of content for realizable matrices on lattice \([0,1]\)
zbMATH Open document ID: 0880.15021
DOI: 10.1016/0165-0114(94)00094-8
author: Xuecheng Liu
published in: Fuzzy Sets and Systems
publication date: 1998-02-08T00:00:00Z
review text: This paper was first presented in BUSEFAL 43, 26-31 (1990). It deals with the max-min decomposition \(B=AA^T\) of a symmetric matrix \(B\) over the semiring \(([0,1],\max,\min)\) [cf. \textit{W. J. Liu}, The realizable problem for an \(F\)-symmetric matrix, Fuzzy Math. (China) 1, 69-75 (1982)]. The author improves recent estimations of the content of a decomposable matrix [cf. e.g. \textit{X. Y. Xue}, BUSEFAL 26, 67-74 (1986; Zbl 0606.15009)] and presents an algorithm for the extremal decomposition. Further results on the decompositions of symmetric matrices were presented by \textit{H. X. Wang} [J. Fuzzy Math. 2, No. 3, 477-494 (1994; Zbl 0819.15013)].
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1022518
zbMATH Keywords: relation matrix
zbMATH Keywords: realizable matrix
zbMATH Keywords: matrix content
zbMATH Keywords: max-min decomposition
zbMATH Keywords: symmetric matrix
zbMATH Keywords: algorithm
zbMATH Keywords: extremal decomposition
reviewed by: Józef Drewniak
MaRDI profile type: Publication
full work available at URL: 0165-0114(94)00094-8
OpenAlex ID: W2014137574
cites work: Q3684239
cites work: Q3783340
cites work: Q5185031
description: scientific article; zbMATH DE number 1022518