Invertible matrices and semilinear spaces over commutative semirings

Information Sciences

Volumn 180, Issue 24, 2010, Pages 5115-5124

  Zhao, Shan ^a   Wang, Xue Ping ^a  

^a SICHUAN NORMAL UNIVERSITY   (China)

Author keywords

Basis; Commutative semiring; Invertible matrix; Linear independence; Semilinear space

Indexed keywords

BASIS; INVERTIBLE MATRICES; LINEAR INDEPENDENCE; SEMI-RING; SEMILINEAR;

VECTOR SPACES;

MATRIX ALGEBRA;

EID: 77957660084     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2010.08.033     Document Type: Article

References (33)

1. F.L. Baccelli, and I. Mairesse Ergodic theorems for stochastic operators and discrete event networks Journal Gunawardena, Idempotency (Bristol, 1994), Publ. Newton Inst Vol. 11 1998 Cambridge University Press Cambridge 171 208
2. R.K. Brouwer A method of relational fuzzy clustering based on producing feature vectors using FastMap Information Sciences 179 2009 3561 3582
3. Z.Q. Cao, K.H. Kim, and F.W. Roush Incline Algebra and Applications 1984 Ellis Horwood Ltd, J. Wiley Chichester, New York
4. K. Cechlárová, and J. Plávka Linear independence in bottleneck algebras Fuzzy Sets and Systems 77 1996 337 348
5. C.C. Chang Algebraic analysis of many valued logics Trans. AMS 93 1958 74 80
6. R.A. Cuninghame-Green Minimax algebra Lecture Notes in Economics and Mathematical Systems Vol. 166 1979 Springer Berlin
7. R.A. Cuninghame-Green, and P. Butkovic Bases in max-algebra Linear Algebra and its Applications 389 2004 107 120
8. A. Di Nola, A. Lettieri, I. Perfilieva, and V. Novak Algebraic analysis of fuzzy systems Fuzzy Sets and Systems 158 2007 1 22
9. D. Dolzan, and P. Oblak Invertible and nilpotent matrices over antirings Linear Algebra and its Applications 430 2009 271 278
10. S. Ghazinoory, A. Esmail Zadeh, and A.S. Kheirkhah Application of fuzzy calculations for improving portfolio matrices Information Sciences 180 2010 1582 1590
11. S. Ghosh Matrices over semirings Information and Sciences 90 1996 221 230
12. Y. Give'on Lattice matrices Information and Control 7 1964 477 484
13. J.S. Golan Semirings and Their Applications 1999 Kluwer Academic Publishers Dordrecht
14. M. Gondran, and M. Minoux Linear algebra in dioïds: a survey of recent results Annals of Discrete Mathematics 19 1984 147 164
15. M. Gondran, and M. Minoux Dioïds and semirings: links to fuzzy sets and other applications Fuzzy Sets and Systems 158 2007 1273 1294
16. M. Gondran, and M. Minoux Graphs Dioïds and Semirings 2008 Springer
17. S.C. Han, and H.X. Li Invertible incline matrices and Cramer's rule over inclines Linear Algebra and its Applications 389 2004 121 138
18. K.H. Kim, and F.W. Roush Generalized fuzzy matrices Fuzzy Sets and Systems 4 1980 293 315
19. R.D. Luce A note on Boolean matrix theory Proceedings of the American Mathematical Society 3 1952 382 388
20. M. Minoux Bideterminants, arborescences and extension of the matrix-tree theorem to semirings Discrete Mathematics 171 1997 191 200
21. M. Minoux A generalization of the all minors matrix tree theorem to semirings Discrete Mathematics 199 1998 139 150
22. H. Nobuhara, D.B.K. Trieu, T. Maruyama, and B. Bede Max-plus algebra-based wavelet transforms and their FPGA implementation for image coding Information Sciences 180 2010 3232 3247
23. I. Perfilieva, Semi-linear spaces, in: H. Noguchi, H. Ishii, et al. (Eds.), Proceedings of Seventh Czech-Japanese Seminar on Data Analysis and Decision Making under Uncertainty, Hyogo, Japan, 2004, pp. 127-130.
24. P.L. Poplin, and R.E. Hartwig Determinantal identities over commutative semirings Linear Algebra and its Applications 387 2004 99 132
25. O.A. Pshenitsyna Factor and term ranks for matrix union over semirings Journal of Mathematical Sciences 5 2006 3384 3399
26. C. Reutenauer, and H. Straubing Inversion of matrices over a commutative semiring Journal of Algebra 88 1984 350 360
27. S. Rudeanu, and D. Vaida Semirings in operations research and computer science: more algebra Fundamenta Informaticae 61 2004 61 85
28. D.E. Rutherford Inverses of Boolean matrices Proceedings of the Glasgow Mathematical Association 6 1963 49 53
29. Z. Xu A method based on distance measure for interval-valued intuitionistic fuzzy group decision making Information Sciences 180 2010 181 190
30. Y.J. Tan On invertible matrices over antirings Linear Algebra and its Applications 423 2007 428 444
31. C.K. Zhao Inverses of L-fuzzy matrices Fuzzy Sets and Systems 34 1990 103 116
32. X.Z. Zhao, Y.B. Jun, and F. Ren The semiring of matrices over a finite chain Information Sciences 178 2008 3443 3450
33. U. Zimmermann Linear and combinatorial optimization in ordered algebraic structures Annals of Discrete Mathematics 10 1981