Journal of Applied Mathematics
Volume 2011 (2011), Article ID 164371, 16 pages
http://dx.doi.org/10.1155/2011/164371
Research Article

On Generalized Transitive Matrices

Jing Jiang,1,2 Lan Shu,1 and Xinan Tian3

1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2Mathematics and Statistics College, Chongqing University of Arts and Sciences, Chongqing 402160, China
3Modern Education Technology Center, Chongqing University of Arts and Sciences, Chongqing 402160, China

Received 9 April 2011; Accepted 5 September 2011

Academic Editor: Vu Phat

Copyright © 2011 Jing Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Transitivity of generalized fuzzy matrices over a special type of semiring is considered. The semiring is called incline algebra which generalizes Boolean algebra, fuzzy algebra, and distributive lattice. This paper studies the transitive incline matrices in detail. The transitive closure of an incline matrix is studied, and the convergence for powers of transitive incline matrices is considered. Some properties of compositions of incline matrices are also given, and a new transitive incline matrix is constructed from given incline matrices. Finally, the issue of the canonical form of a transitive incline matrix is discussed. The results obtained here generalize the corresponding ones on fuzzy matrices and lattice matrices shown in the references.