Ultra LI-ideals in lattice implication algebras and MTL-algebras

Czechoslovak Mathematical Journal

Volumn 57, Issue 2, 2007, Pages 591-605

  Zhang, Xiaohong ^a,d   Qin, Keyun ^b,d   Dudek, Wiesław A ^c,d  

^a NINGBO UNIVERSITY   (China)

^b SOUTHWEST JIAOTONG UNIVERSITY   (China)

^c WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^d NONE

Author keywords

(prime, ultra, obstinate, Boolean) LI ideal; ILI ideal; Lattice implication algebra; MTL algebra

Indexed keywords

EID: 50349092469     PISSN: 00114642     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10587-007-0100-6     Document Type: Article

References (18)

1. R. Bělohlávek 2003 Some properties of residuated lattices Czechoslovak Math. J. 53 128 161 171 (Pubitemid 36914080)
2. W. A. Dudek X. H. Zhang 1998 On ideals and congruences in BCC-algebras Czechoslovak Math. J. 48 123 21 29
3. F. Esteva L. Godo 2001 Monoidal t-norm based logic: Towards a logic for left-continuous t-norms Fuzzy Sets Syst. 124 271 288 (Pubitemid 32951435)
4. P. Hájek: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, 1998.
5. S. Jenei F. Montagna 2002 A proof of standard completeness for Esteva and Godo's logic MTL Studia Logica 70 183 192
6. Y. B. Jun 1999 On LI-ideals and prime LI-ideals of lattice implication alebras J. Korean Math. Soc. 36 369 380
7. Y. B. Jun E. H. Roh Y. Xu 1998 LI-ideals in lattice implication algebras Bull. Korean Math. Soc. 35 13 24
8. Y. B. Jun Y. Xu 1999 Fuzzy LI-ideals in lattice implication algebras J. Fuzzy Math. 7 997 1003
9. Y. L. Liu S.Y. Liu Y. Xu K.Y. Qin 2003 ILI-ideals and prime LI-ideals in lattice implication algebras Information Sciences 155 157 175
10. C. Noguera F. Esteva J. Gispert 2005 On some varieties of MTL-algebras Log. J. IGPL 13 443 466 (Pubitemid 44592784)
11. K.Y. Qin Y. Xu Y. B. Jun 2002 Ultra LI-ideals in lattice implication algebras Czechoslovak Math. J. 52 127 463 468 (Pubitemid 36100762)
12. E. Turunen 2001 Boolean deductive systems of BL-algebras Arch. Math. Logic 40 467 473
13. G. J. Wang: Non-classical Mathematical Logic and Approximate Reasoning. Science Press, Beijing, 2000. (In Chinese.)
14. 0-algebras and multiple-valued logic Fuzzy Systems and Mathematics 16 1 15
15. Y. Xu 1993 Lattice implication algebras J. South West Jiaotong University 1 20 27
16. Y. Xu K.Y. Qin 1993 On filters of lattice implication algebras J. Fuzzy Math. 1 251 260
17. Y. Xu, D. Ruan, K.Y. Qin, J. Li: Lattice-valued Logic. An alternative approach to treat fuzziness and incomparability. Studies in Fuzzines and Soft Computing 132. Springer-Verlag, 2003.
18. X. H. Zhang W. H. Li 2005 On fuzzy logic algebraic system MTL Advances in Systems and Applications 5 475 483