On simultaneously nilpotent fuzzy matrices

Yung Yih Lur; Chin Tzong Pang; Sy Ming Guu

doi:10.1016/S0024-3795(02)00587-6

On simultaneously nilpotent fuzzy matrices

Yung Yih Lur
, Chin Tzong Pang
, Sy Ming Guu^*

^*Corresponding author for this work

Van Nung Institute of Technology Taiwan
Yuan Ze University

Research output: Contribution to journal › Journal Article › peer-review

14 Scopus citations

Abstract

Nilpotent fuzzy matrices play a crucial role in the study of fuzzy matrices. In this paper, we shall extend the nilpotence to the notion of simultaneous nilpotence for a finite set of fuzzy matrices. The notion of simultaneous nilpotence relates to the infinite products of a finite number of fuzzy matrices which converge to the zero matrix. Properties of the simultaneous nilpotence will be established. In the study of consecutive powers of a fuzzy matrix, a controllable fuzzy matrix can be characterized by an associated nilpotent fuzzy matrix. In this paper, we propose the notion of simultaneously controllable fuzzy matrices which can be thought of as a generalization of the notion of controllable fuzzy matrices. Similar to the nilpotent characterization for a controllable fuzzy matrix, the simultaneously controllable fuzzy matrices can be characterized by a finite set of associated simultaneously nilpotent fuzzy matrices.

Original language	English
Pages (from-to)	37-45
Number of pages	9
Journal	Linear Algebra and Its Applications
Volume	367
DOIs	https://doi.org/10.1016/S0024-3795(02)00587-6
State	Published - 01 07 2003
Externally published	Yes

Keywords

Boolean matrices
Fuzzy matrices
Simultaneous nilpotence
Simultaneously controllable

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10.1016/S0024-3795(02)00587-6

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AU - Lur, Yung Yih

AU - Pang, Chin Tzong

AU - Guu, Sy Ming

PY - 2003/7/1

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N2 - Nilpotent fuzzy matrices play a crucial role in the study of fuzzy matrices. In this paper, we shall extend the nilpotence to the notion of simultaneous nilpotence for a finite set of fuzzy matrices. The notion of simultaneous nilpotence relates to the infinite products of a finite number of fuzzy matrices which converge to the zero matrix. Properties of the simultaneous nilpotence will be established. In the study of consecutive powers of a fuzzy matrix, a controllable fuzzy matrix can be characterized by an associated nilpotent fuzzy matrix. In this paper, we propose the notion of simultaneously controllable fuzzy matrices which can be thought of as a generalization of the notion of controllable fuzzy matrices. Similar to the nilpotent characterization for a controllable fuzzy matrix, the simultaneously controllable fuzzy matrices can be characterized by a finite set of associated simultaneously nilpotent fuzzy matrices.

AB - Nilpotent fuzzy matrices play a crucial role in the study of fuzzy matrices. In this paper, we shall extend the nilpotence to the notion of simultaneous nilpotence for a finite set of fuzzy matrices. The notion of simultaneous nilpotence relates to the infinite products of a finite number of fuzzy matrices which converge to the zero matrix. Properties of the simultaneous nilpotence will be established. In the study of consecutive powers of a fuzzy matrix, a controllable fuzzy matrix can be characterized by an associated nilpotent fuzzy matrix. In this paper, we propose the notion of simultaneously controllable fuzzy matrices which can be thought of as a generalization of the notion of controllable fuzzy matrices. Similar to the nilpotent characterization for a controllable fuzzy matrix, the simultaneously controllable fuzzy matrices can be characterized by a finite set of associated simultaneously nilpotent fuzzy matrices.

KW - Boolean matrices

KW - Fuzzy matrices

KW - Simultaneous nilpotence

KW - Simultaneously controllable

UR - https://www.scopus.com/pages/publications/0038057799

U2 - 10.1016/S0024-3795(02)00587-6

DO - 10.1016/S0024-3795(02)00587-6

M3 - 文章

AN - SCOPUS:0038057799

SN - 0024-3795

VL - 367

SP - 37

EP - 45

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

On simultaneously nilpotent fuzzy matrices

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Keywords

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