The period of powers of a fuzzy matrix
type: Item
instance of: scholarly article
title: The period of powers of a fuzzy matrix
zbMATH Open document ID: 0980.15014
DOI: 10.1016/S0165-0114(98)00080-3
author: Hideyuki Imai
author: Yuichiro Okahara
author: Masaaki Miyakoshi
published in: Fuzzy Sets and Systems
publication date: 2002-02-20T00:00:00Z
review text: An \(n{\times}n\) matrix \(A = (a_{ij})\) whose components are in the unit interval \([0,1]\) is called a fuzzy matrix. A fuzzy matrix plays an important role in system models based on a fuzzy relation, and the performance of such a system depends on forming powers of a fuzzy matrix. The powers of a general fuzzy matrix either converge or oscillate with a finite period. Many properties about convergence have been investigated, for example, sufficient conditions for convergence are shown. Moreover, a lot of properties about convergence of powers of a transitive fuzzy matrix have been considered. However, few investigations about the period have been made. The authors consider the period of the powers of a general fuzzy matrix by a graph theoretical viewpoint, and they state conditions for convergence under the max-min composition.
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1423391
zbMATH Keywords: fuzzy matrix
zbMATH Keywords: max-min composition
zbMATH Keywords: graph theory
zbMATH Keywords: cycle
zbMATH Keywords: period
zbMATH Keywords: convergence
zbMATH Keywords: fuzzy relation
zbMATH Keywords: powers
reviewed by: Nikolai I. Osetinski
MaRDI profile type: Publication
full work available at URL: s0165-0114(98)00080-3
OpenAlex ID: W2075516699
Wikidata QID: Q128066590
description: scientific article; zbMATH DE number 1423391