On nilpotent matrices over distributive lattices

Fuzzy Sets and Systems

Volumn 151, Issue 2, 2005, Pages 421-433

  Tan, Yi Jia ^a  

^a FUZHOU UNIVERSITY   (China)

Author keywords

Adjoint matrix; Distributive lattice; Nilpotent matrix; Reduction of matrix

Indexed keywords

BOOLEAN ALGEBRA; FUNCTIONS; GRAPH THEORY; MATHEMATICAL MODELS; MATRIX ALGEBRA; THEOREM PROVING;

ADJOINT MATRIX; DISTRIBUTIVE LATTICES; FUZZY ALGEBRA; NILPOTENT MATRIX;

FUZZY SETS;

EID: 13644258651     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2004.06.009     Document Type: Article

References (17)

1. G. Birkhoff Lattice Theory 3rd ed. 1967 Amer. Math. Soc. Providence, RI
2. K. Cechlárová Powers of matrices over distributive lattices - a review Fuzzy Sets and Systems 138 2003 627 641
3. A.C. Fisher, J.S. Liebmain, and G.L. Nemhauser Computer construction of project networks Comm. ACM 11 1968 493 497
4. Y. Give'on Lattice matrices Inform. Control 7 1964 477 484
5. J.A. Goguen L-fuzzy sets J. Math. Anal. Appl. 18 1967 145 174
6. G. Grätzer General Lattice Theory 2nd ed. 1998 Birkhäuser Verlag Basel, Boston, Berlin
7. F. Harary On the consistency of precedence matrices J. Assoc. Comput. Math. 7 1960 255 259
8. H. Hashimoto Reduction of a nilpotent fuzzy matrix Inform. Sci. 27 1982 223 243
9. J.X. Li Some results on the nilpotent fuzzy matrices Fuzzy Systems Math. 3 1989 52 55 (in Chinese)
10. Y.Y. Lur, C.T. Pang, S.M. Guu, On the nilpotent fuzzy matrices, Fuzzy Sets and Systems, to appear
11. R.B. Marimont A new method of checking the consistency of precedence matrices J. Assoc. Comput. Math. 6 1959 164 171
12. S.V. Ovchinnikov Structure of fuzzy binary relations Fuzzy Sets and Systems 6 1981 169 195
13. H.T. Ren, Z. Zhang, and Z.S. Liu A necessary and sufficient condition for nilpotent fuzzy matrices Acta Sci. Natur. Univ. Nei Monggol 27 1996 594 596 (in Chinese)
14. Y.J. Tan On the powers of matrices over a distributive lattice Linear Algebra Appl. 336 2001 1 14
15. Y.J. Tan On compositions of lattice matrices Fuzzy Sets and Systems 129 2002 19 28
16. K.L. Zhang Determinant theory for D 01 -lattice matrices Fuzzy Sets and Systems 62 1994 347 353
17. K.L. Zhang On the nilpotent matrices over D 01 -lattice Fuzzy Sets and Systems 117 2001 403 406