A note on the power sequence of a fuzzy matrix
type: Item
instance of: scholarly article
title: A note on the power sequence of a fuzzy matrix
zbMATH Open document ID: 0939.15011
DOI: 10.1016/S0165-0114(97)00118-8
published in: Fuzzy Sets and Systems
publication date: 2000-07-02T00:00:00Z
review text: The author examines the min-max product of matrices over the semiring ([0, 1], min, max) [cf. \textit{M. Z. Ragab} and \textit{F. G. Emam}, Fuzzy Sets Syst. 75, No. 1, 83-92 (1995; Zbl 0860.15013)] as a dual of the usually used max-min product. This provides dual versions of known results. Next, the convergence of the matrix powers sequence under sup-t-norm composition is characterized. However, the author changes the well-known definition of triangular norms [Definition 1; cf. \textit{B. Schweizer} and \textit{A. Sklar}, Probabilistic metric spaces (North-Holland, Amsterdam) (1983; Zbl 0546.60010), Definition 5.5.1] which can generate misunderstandings in applications of his results. Similarly, in Definition 6 the Archimedean triangular norm is called a zero-t-norm. Remark: In general the S-T composition from Definition 4 is not associative (e.g. for \[ S(x,y) = x + y - xy,\;T(x,y) = xy,\;x, y \in [0,1]), \] which is necessary for the unique definition of matrix powers in Definition 5.
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1339537
zbMATH Keywords: triangular norm
zbMATH Keywords: semiring
zbMATH Keywords: min-max composition
zbMATH Keywords: min-max powers
zbMATH Keywords: sup-T composition
zbMATH Keywords: convergence
zbMATH Keywords: power sequence
zbMATH Keywords: fuzzy matrix
author: Zhou Tian Fan
reviewed by: Józef Drewniak
MaRDI profile type: Publication
cites work: Q4224429
cites work: Q3822103
cites work: On the min-max composition of fuzzy matrices
full work available at URL: s0165-0114(97)00118-8
OpenAlex ID: W2024733227
description: scientific article; zbMATH DE number 1339537