On the Convergence of Monotone Lattice Matrices

Affiliation(s)

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, China.

The College of Mathematics and Statistics, Chongqing University of Arts and Sciences, Chongqing, China.

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, China.

The College of Mathematics and Statistics, Chongqing University of Arts and Sciences, Chongqing, China.

ABSTRACT

Since lattice matrices are useful tools in various domains like automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control and so on, the study of the properties of lattice matrices is valuable. A lattice matrix*A*** **is called monotone if *A* is transitive or *A* is monotone increasing. In this paper, the convergence of monotone matrices is studied. The results obtained here develop the corresponding ones on lattice matrices shown in the references.

Since lattice matrices are useful tools in various domains like automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control and so on, the study of the properties of lattice matrices is valuable. A lattice matrix

Cite this paper

J. Jiang, L. Shu and X. Tian, "On the Convergence of Monotone Lattice Matrices,"*Applied Mathematics*, Vol. 4 No. 6, 2013, pp. 903-906. doi: 10.4236/am.2013.46125.

J. Jiang, L. Shu and X. Tian, "On the Convergence of Monotone Lattice Matrices,"

References

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[1] F. A. Deng and S. Y. Liu, “Application of Fuzzy Concept Networks in Fault Diagnosis,” Control and Decision, Vol. 16, 2001, pp. 834-836.

[2] S. V. Ovchinnikov, “Structure of Fuzzy Binary Relations,” Fuzzy Sets and Systems, Vol. 6, No. 2, 1981, pp. 169-195. doi:10.1016/0165-0114(81)90023-3

[3] V. Tahani, “A Fuzzy Model of Document Retrieval Systems,” Information Processing Management, Vol. 12, No. 3, 1976, pp. 177-187. doi:10.1016/0306-4573(76)90004-2

[4] F. Harary, “On the Consistency of Precedence Matrices,” Journal of the ACM, Vol. 7, No. 3, 1960, pp. 255-259. doi:10.1145/321033.321038

[5] Y. J. Tan, “On the Power of Matrices over a Distributive Lattice,” Linear Algebra and Its Applications, Vol. 336, 2001, pp. 1-14. doi:10.1016/j.laa.2004.11.016

[6] Y. J. Tan, “On the Transitive Matrices over Distributive Lattices,” Linear Algebra and Its Applications, Vol. 400, 2005, pp. 169-191.