Linear independence in bottleneck algebras
type: Item
instance of: scholarly article
title: Linear independence in bottleneck algebras
zbMATH Open document ID: 0877.15017
DOI: 10.1016/0165-0114(95)00052-6
author: Ján Plavka
author: Katarina Cechlárová
published in: Fuzzy Sets and Systems
publication date: 1997-12-10T00:00:00Z
review text: The paper presents ten diverse generalizations of the definition of vector independence over a field to that over a lattice used in recent literature [cf. e.g. \textit{M. Gondran} and \textit{M. Minoux}, L'indépendance linéaire dans les dioides, Bull. Dir. Etudes Rech., Sér. C Math. Inform. 38-48 (1978); \textit{K. H. Kim} and \textit{F. W. Roush}, Fuzzy Sets Syst. 4, 293-315 (1980; Zbl 0451.20055); \textit{P. Butkovič}, \textit{K. Cechlárová} and \textit{P. Szabó}, Linear Algebra Appl. 94, 133-155 (1987; Zbl 0629.90093)]. Precisely, a max-min dependence of vectors over the semiring \(([0,1]\), max, min) is discussed. Many characterizations and interrelations of these definitions are proved.
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 1004752
zbMATH Keywords: bottleneck algebras
zbMATH Keywords: fuzzy matrix
zbMATH Keywords: max-min product
zbMATH Keywords: max-min dependence
zbMATH Keywords: linear dependence
zbMATH Keywords: matrix rank
zbMATH Keywords: permanent
reviewed by: Józef Drewniak
MaRDI profile type: Publication
full work available at URL: 0165-0114(95)00052-6
OpenAlex ID: W2045667604
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description: scientific article; zbMATH DE number 1004752