- Volume 55 Issue 4
The notion of quasi-valuation maps based on a subalgebra and an ideal in BCK/BCI-algebras is introduced, and then several properties are investigated. Relations between a quasi-valuation map based on a subalgebra and a quasi-valuation map based on an ideal is established. In a BCI-algebra, a condition for a quasi-valuation map based on an ideal to be a quasi-valuation map based on a subalgebra is provided, and conditions for a real-valued function on a BCK/BCI-algebra to be a quasi-valuation map based on an ideal are discussed. Using the notion of a quasi-valuation map based on an ideal, (pseudo) metric spaces are constructed, and we show that the binary operation * in BCK-algebras is uniformly continuous.
BCK/BCI-algerba;subalgebra;ideal;S-quasi-valuation map;I-quasi-valuation map;(pseudo) metric space;uniformly continuous
- Y. S. Huang, BCI-algebra, Science Press, China (2006).
- Y. Imai and K. Iseki, On axiom systems of propositional calculi. XIV, Proc. Japan Acad., 42(1966), 19-22.
- K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad., 42(1966), 26-29. https://doi.org/10.3792/pja/1195522171
- K. Iseki, On BCI-algebras, Math. Seminar Notes, 8(1980), 125-130.
- K. Iseki and S. Tanaka, An introduction to theory of BCK-algebras, Math. Japonica, 23(1978), 1-26.
- J. Meng, Y. B. Jun, BCK-algebras, Kyungmoon Sa Co., Seoul (1994).
- J. Neggers, A. Dvurecenskij and H. S. Kim, On d-fuzzy functions in d-algebras, Found. Phys., 30(2000), 1807-1816. https://doi.org/10.1023/A:1026466720971
- J. Neggers, Y. B. Jun, H. S. Kim, On d-ideals in d-algebras, Math. Slovaca, 49(1999), 243-251.
- J. Neggers, H. S. Kim, On d-algebras, Math. Slovaca, 49(1999), 19-26.
- L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Inform. Sci., 172(2005), 1-40. https://doi.org/10.1016/j.ins.2005.01.017
연구 과제 주관 기관 : Jeju National University