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http://dx.doi.org/10.5666/KMJ.2015.55.4.859

Quasi-Valuation Maps on BCK/BCI-Algebras  

SONG, SEOK-ZUN (Department of Mathematics, Jeju National University)
ROH, EUN HWAN (Department of Mathematics Education, Chinju National University of Education)
JUN, YOUNG BAE (Department of Mathematics Education, Gyeongsang National University)
Publication Information
Kyungpook Mathematical Journal / v.55, no.4, 2015 , pp. 859-870 More about this Journal
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;
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  • Reference
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.   DOI
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.   DOI
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.   DOI