Construction of $ BCK $-neighborhood systems in a $ d $-algebra

Hee Sik Kim; J. Neggers; Sun Shin Ahn; Hee Sik Kim; J. Neggers; Sun Shin Ahn

doi:10.3934/math.2021547

AIMS Mathematics

2021, Volume 6, Issue 9: 9422-9435. doi: 10.3934/math.2021547

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Construction of $ BCK $-neighborhood systems in a $ d $-algebra

1.
Department of Mathematics, Hanyang University, Seoul 04763, Korea
2.
Department of Mathematics, University of Alabama, Tuscaloosa, AL, 35487-0350, U.S.A
3.
Department of Mathematics Education, Dongguk University, Seoul 04620, Korea

Received: 20 April 2021 Accepted: 07 June 2021 Published: 23 June 2021
MSC : 06F35, 20N02

The $ BCK $-neighborhood systems in $ d $-algebras as measures of distance of these algebras from $ BCK $-algebras is introduced. We consider examples of various cases and situations related to the general theory, as well as a compilcated analytical example of one of particular interest in the theory of pseudo-$ BCK $-algebras. It appears also that a digraph theory may play a constructive role in this case as it dose in the theory of $ BCK $-algebras.
- $ BCK $-neighborhood system,
- $ d $-algebra
Citation: Hee Sik Kim, J. Neggers, Sun Shin Ahn. Construction of $ BCK $-neighborhood systems in a $ d $-algebra[J]. AIMS Mathematics, 2021, 6(9): 9422-9435. doi: 10.3934/math.2021547

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Abstract

The $ BCK $-neighborhood systems in $ d $-algebras as measures of distance of these algebras from $ BCK $-algebras is introduced. We consider examples of various cases and situations related to the general theory, as well as a compilcated analytical example of one of particular interest in the theory of pseudo-$ BCK $-algebras. It appears also that a digraph theory may play a constructive role in this case as it dose in the theory of $ BCK $-algebras.

References

[1]	P. J. Allen, H. S. Kim, J. Neggers, Companion $d$-algebras, Math. Slovaca., 57 (2007), 93–106. doi: 10.2478/s12175-007-0001-z
[2]	P. J. Allen, H. S. Kim, J. Neggers, Deformations of d/BCK-algebras, Bull. Korean Math. Soc., 48 (2011), 315–324. doi: 10.4134/BKMS.2011.48.2.315
[3]	Y. Huang, BCI-algebras, Beijing: Science Press, 2006.
[4]	A. Iorgulescu, Algebras of logic as $BCK$-algebras, Bucharest: Editura ASE, 2008.
[5]	K. Iséki, On $BCI$-algebras, Math. Semin. Notes, 8 (1980), 125–130.
[6]	K. Iséki, S. Tanaka, An introduction to theory of $BCK$-algebras, Math. Japonicae, 23 (1978), 1–26.
[7]	H. S. Kim, J. Neggers, K. S. So, Some aspects of $d$-units in $d/BCK$-algebras, Jour. Appl. Math., 2012 (2012), 1–10.
[8]	J. Meng, Y. B. Jun, $BCK$-algebras, Seoul: Kyungmoon Sa, 1994.
[9]	J. Neggers, Y. B. Jun, H. S. Kim, On $d$-ideals in $d$-algebras, Math. Slovaca, 49 (1999), 243–251.
[10]	J. Neggers, H. S. Kim, On $d$-algebras, Math. Slovaca, 49 (1999), 19–26.

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