On Generalized Transitive Matrices | Zendy

Jing Jiang | Zendy; Lan Shu | Zendy; Xinan Tian | Zendy

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On Generalized Transitive Matrices

Author(s) -

Jing Jiang,

Lan Shu,

Xinan Tian

Publication year - 2011

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2011/164371

Subject(s) - transitive closure , mathematics , transitive relation , pure mathematics , semiring , transitive reduction , matrix (chemical analysis) , matrix analysis , algebra over a field , discrete mathematics , combinatorics , eigenvalues and eigenvectors , graph , materials science , physics , line graph , quantum mechanics , composite material , voltage graph

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, anddistributive 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 transitiveincline matrices is considered. Some properties of compositions of incline matrices are alsogiven, 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 shownin the references

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