Journal of Applied Mathematics

On Generalized Transitive Matrices

Jing Jiang, Lan Shu, and Xinan Tian

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

First available in Project Euclid: 15 March 2012

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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.

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