PDF
Discussiones
Mathematicae General Algebra and Applications 20(1) (2000) 77-86
DOI: https://doi.org/10.7151/dmgaa.1007
ON FUZZY TOPOLOGICAL BCC-ALGEBRAS
Wiesław A. Dudek Institute of Mathematics Technical University |
Young Bae Jun and Sung Min Hong Department of Mathematics Education |
Abstract
We describe properties of subalgebras and BCC-ideals in BCC-algebras with a topology induced by a family of fuzzy sets.
Keywords: BCC-algebra, fuzzy subalgebra, fuzzy topological subalgebra.
1991 Mathematics Subject Classification: 06F35, 03G25, 94D05.
References
| [1] | W.A. Dudek, The number of subalgebras of finite BCC-algebras, Bull. Inst. Math. Acad. Sinica 20 (1992), 129-136. |
| [2] | W.A. Dudek, On proper BCC-algebras, Bull. Inst. Math. Acad. Sinica 20 (1992), 137-150. |
| [3] | W.A. Dudek and Y.B. Jun, Fuzzy BCC-ideals in BCC-algebras, Math. Montisnigri 10 (1999), 21-30. |
| [4] | W.A. Dudek and X.H. Zhang, On ideals and congruences in BCC-algebras, Czechoslovak Math. J. 48 (123) (1998), 21- 29. |
| [5] | D.H. Foster, Fuzzy topological groups, J. Math. Anal. Appl. 67 (1979), 549-564. |
| [6] | Y. Imai and K. Iséki, On axiom system of propositional calculi XIV, Proc. Japan Acad. 42 (1966), 19-22. |
| [7] | K. Iséki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. 23 (1978), 1-26. |
| [8] | Y. Komori, The class of BCC-algebras is not a variety, Math. Japon. 29 (1984), 391-394. |
| [9] | J. Meng and Y. B. Jun, BCK-algebras, Kyungmoonsa, Seoul, Korea 1994. |
| [10] | A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517. |
| [11] | A. Wroński, BCK-algebras do not form a variety, Math. Japon. 28 (1983), 211-213. |
| [12] | L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. |
Received 3 September 1998
Revised 26 March 1999
Close