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2011 On Generalized Transitive Matrices
Jing Jiang, Lan Shu, Xinan Tian
J. Appl. Math. 2011: 1-16 (2011). DOI: 10.1155/2011/164371


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.


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Jing Jiang. Lan Shu. Xinan Tian. "On Generalized Transitive Matrices." J. Appl. Math. 2011 1 - 16, 2011.


Published: 2011
First available in Project Euclid: 15 March 2012

zbMATH: 1235.15027
MathSciNet: MR2846441
Digital Object Identifier: 10.1155/2011/164371

Rights: Copyright © 2011 Hindawi


Vol.2011 • 2011
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