Journal of Applied Mathematics

On Generalized Transitive Matrices

Jing Jiang, Lan Shu, and Xinan Tian

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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.

Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 164371, 16 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331818655

Digital Object Identifier
doi:10.1155/2011/164371

Mathematical Reviews number (MathSciNet)
MR2846441

Zentralblatt MATH identifier
1235.15027

Citation

Jiang, Jing; Shu, Lan; Tian, Xinan. On Generalized Transitive Matrices. J. Appl. Math. 2011 (2011), Article ID 164371, 16 pages. doi:10.1155/2011/164371. https://projecteuclid.org/euclid.jam/1331818655


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