Simultaneously controllable fuzzy matrices
type: Item
instance of: scholarly article
title: Simultaneously controllable fuzzy matrices
zbMATH Open document ID: 1100.15008
author: Chin-Tzong Pang
publication date: 2006-02-02T00:00:00Z
review text: The paper deals with multiple max-min products of matrices over the lattice ([0,1],max,min) (fuzzy matrices). The canonical form of fuzzy matrices was proposed by \textit{K. H. Kim} and \textit{F. W. Roush} [Fuzzy Sets Syst. 4, 293--315 (1980; Zbl 0451.20055)] and examined by \textit{H. Hashimoto} [Fuzzy Sets Syst. 11, 157--162 (1983; Zbl 0523.15013)], \textit{X. T. Peng} [Fuzzy Sets Syst. 19, 47--50 (1986; Zbl 0606.15008)], \textit{W. Kołodziejczyk} [Fuzzy Sets Syst. 22, 297--302 (1987; Zbl 0623.15019)] and \textit{Ch. Hao} [Fuzzy Sets Syst. 45, 219--222 (1992; Zbl 0752.15017)]. A characterization of such matrices was obtained by \textit{J. X. Li} [Fuzzy Sets Syst. 45, 313--319 (1992; Zbl 0749.15014)] under the new name `controllable fuzzy matrices'. As a generalization we have the notion of simultaneous controllable matrices by \textit{Y. Y. Lur} et al. [Linear Algebra Appl. 367, 37--45 (2003; Zbl 1028.15015)]. In this paper the results of Li [loc. cit.] are extended for a family of simultaneously controllable matrices. In particular we have a characterization by the use of nilpotent matrices and an algorithm for checking of simultaneous controllability. These results are used in examination of convergence of mixed products of a family of fuzzy matrices according to the definition by \textit{S. M. Guu, H.-H. Chen} and \textit{C.-T. Pang} [Fuzzy Sets Syst. 121, 203--207 (2001; Zbl 0994.15017)].
reviewed by: Józef Drewniak
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 08A72
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 5003151
zbMATH Keywords: fuzzy matrix
zbMATH Keywords: controllable matrix
zbMATH Keywords: nilpotent matrix
zbMATH Keywords: mixed relation powers
zbMATH Keywords: convergence of powers
zbMATH Keywords: oscillation of powers
zbMATH Keywords: algorithm for checking of controllability
MaRDI profile type: Publication
full work available at URL: j.camwa.2005.06.008
OpenAlex ID: W2017190404
cites work: On the powers of matrices in bottleneck/fuzzy algebra
cites work: Powers of matrices over distributive lattices -- a review
cites work: On the oscillating power sequence of a fuzzy matrix
cites work: Congerence of powers of a fuzzy transitive matrix
cites work: Canonical form of a transitive fuzzy matrix
cites work: Controllable fuzzy matrices
cites work: On the power method in max algebra
cites work: Modifying the power method in max algebra
cites work: A note on the power sequence of a fuzzy matrix
cites work: A note on the sequence of consecutive powers of a nonnegative matrix in max algebra
cites work: On the sequence of consecutive powers of a fuzzy matrix with max-Archimedean-t-norms
cites work: Convergence of powers of a fuzzy matrix
cites work: On infinite products of fuzzy matrices
cites work: On simultaneously nilpotent fuzzy matrices
cites work: Generalized fuzzy matrices
cites work: Q3781511
cites work: Norm conditions for convergence of infinite products
DOI: 10.1016/J.CAMWA.2005.06.008
published in: Computers & Mathematics with Applications
Recommended article: Controllable fuzzy matrices
Recommended article: On Controllability of Fuzzy Dynamical Matrix Lyapunov Systems
Recommended article: Convergence of powers of controllable fuzzy matrices
Recommended article: Algorithm for controllable and nilpotent intuitionistic fuzzy matrices
Recommended article: On controllability and observability of fuzzy dynamical matrix Lyapunov systems
Recommended article: Mathematical Aspects of Fuzzy Control
Recommended article: Q3325574
Recommended article: Controllability of Fuzzy Control Systems
Recommended article: Multivariable Structure of Fuzzy Control Systems
Recommended article: Mathematical Fuzzy Control. A Survey of Some Recent Results
description: scientific article; zbMATH DE number 5003151