EIGENSPACE OF A THREE-DIMENSIONAL MAX-LUKASIEWICZ FUZZY MATRIX

被引：1

作者：

Rashid, Imran ^{[1
]}

Gavalec, Martin ^{[2
]}

Sergeev, Sergei ^{[3
,4
]}

机构：

[1] COMSATS Inst Informat Technol, Abbottabad 22060, Pakistan

[2] Univ Hradec Kralove, Fac Informat & Management, Hradec Kralove 50003, Czech Republic

[3] INRIA, F-91128 Palaiseau, France

[4] CMAP Ecole Polytech, F-91128 Palaiseau, France

来源：

KYBERNETIKA | 2012年 / 48卷 / 02期

关键词：

Lukasiewicz triangular norm; max-t fuzzy algebra; eigenproblem; monotone eigenvector; EIGENVECTORS; EIGENVALUES; ALGEBRA;

D O I：

暂无

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

Eigenvectors of a fuzzy matrix correspond to stable states of a complex discrete-events system, characterized by a given transition matrix and fuzzy state vectors. Description of the eigenspace (set of all eigenvectors) for matrices in max-min or max-drast fuzzy algebra was presented in previous papers. In this paper the eigenspace of a three-dimensional fuzzy matrix in max-Lukasiewicz algebra is investigated. Necessary and sufficient conditions are shown under which the eigenspace restricted to increasing eigenvectors of a given matrix is non-empty, and the structure of the increasing eigenspace is described. Complete characterization of the general eigenspace structure for arbitrary three-dimensional fuzzy matrix, using simultaneous row and column permutations of the matrix, is presented in Sections 4 and 5, with numerical examples in Section 6.

引用

页码：309 / 328

页数：20

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