On simultaneously nilpotent fuzzy matrices
type: Item
instance of: scholarly article
title: On simultaneously nilpotent fuzzy matrices
zbMATH Open document ID: 1028.15015
DOI: 10.1016/S0024-3795(02)00587-6
author: Yanyan Li
published in: Linear Algebra and its Applications
publication date: 2003-05-27T00:00:00Z
review text: The theory of nilpotent fuzzy matrices is developed [cf. \textit{H. Hashimoto}, Fuzzy Sets Syst. 10, 101-108 (1983; Zbl 0512.15014); \textit{J.-X. Li}, ibid. 45, 313-319 (1992; Zbl 0749.15014); ibid. 62, 83-88 (1994; Zbl 0826.15020); \textit{Y.-Y. Lur}, \textit{S.-M. Guu} and \textit{C. S. Pang}, On the eigenvalues of fuzzy matrices. Working paper, Department of Information Management, Yuan Ze Univ. (2001)]. As a generalization, the notions of the simultaneous nilpotence and of the simultaneously controllable fuzzy matrices are introduced. The properties of the simultaneous nilpotence, related to the infinite products of a finite number of fuzzy matrices which converge to the zero matrix, are established. It is also taken into account that in the study on consecutive powers of fuzzy matrices, a controllable fuzzy matrix can be characterized by an associated nilpotent fuzzy matrix. As an analogue, it is shown that the simultaneously controllable fuzzy matrices can be characterized by a finite set of the associated simultaneously nilpotent fuzzy matrices.
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 08A72
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 1917802
zbMATH Keywords: Boolean matrices
zbMATH Keywords: fuzzy matrices
zbMATH Keywords: simultaneous nilpotence
zbMATH Keywords: simultaneously controllable
zbMATH Keywords: controllable fuzzy matrix
reviewed by: A. A. Bogush
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1917802