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Quasi-Valuation Maps on BCK/BCI-Algebras
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 4,  2015, pp.859-870
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.4.859
 Title & Authors
Quasi-Valuation Maps on BCK/BCI-Algebras
SONG, SEOK-ZUN; ROH, EUN HWAN; JUN, YOUNG BAE;
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 Abstract
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.
 Keywords
BCK/BCI-algerba;subalgebra;ideal;S-quasi-valuation map;I-quasi-valuation map;(pseudo) metric space;uniformly continuous;
 Language
English
 Cited by
 References
1.
Y. S. Huang, BCI-algebra, Science Press, China (2006).

2.
Y. Imai and K. Iseki, On axiom systems of propositional calculi. XIV, Proc. Japan Acad., 42(1966), 19-22.

3.
K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad., 42(1966), 26-29. crossref(new window)

4.
K. Iseki, On BCI-algebras, Math. Seminar Notes, 8(1980), 125-130.

5.
K. Iseki and S. Tanaka, An introduction to theory of BCK-algebras, Math. Japonica, 23(1978), 1-26.

6.
J. Meng, Y. B. Jun, BCK-algebras, Kyungmoon Sa Co., Seoul (1994).

7.
J. Neggers, A. Dvurecenskij and H. S. Kim, On d-fuzzy functions in d-algebras, Found. Phys., 30(2000), 1807-1816. crossref(new window)

8.
J. Neggers, Y. B. Jun, H. S. Kim, On d-ideals in d-algebras, Math. Slovaca, 49(1999), 243-251.

9.
J. Neggers, H. S. Kim, On d-algebras, Math. Slovaca, 49(1999), 19-26.

10.
L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Inform. Sci., 172(2005), 1-40. crossref(new window)