Length Neutrosophic Subalgebras of BCK=BCI-Algebras

Young Bae Jun; Madad Khan; Florentin Smarandache; Seok-Zun Song

doi:10.18778/0138-0680.2020.21

Authors

Young Bae Jun Gyeongsang National University Department of Mathematics Education Jinju 52828, Korea Author http://orcid.org/0000-0002-0181-8969
Madad Khan COMSATS Institute of Information Technology Department of Mathematics Abbottabad, Pakistan Author http://orcid.org/0000-0003-0044-961X
Florentin Smarandache University of New Mexico Department of Mathematics New Mexico 87301, USA Author http://orcid.org/0000-0002-5560-5926
Seok-Zun Song Jeju National University Department of Mathematics Jeju 63243, Korea Author http://orcid.org/0000-0002-2383-664X

DOI:

https://doi.org/10.18778/0138-0680.2020.21

Keywords:

interval neutrosophic set, interval neutrosophic length, length neutrosophic subalgebra

Abstract

Given i, j, k ∈ {1,2,3,4}, the notion of (i, j, k)-length neutrosophic subalgebras in BCK=BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.

References

[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 20(1) (1986), pp. 87–96, DOI: http://dx.doi.org/10.1016/S0165-0114(86)80034-3 DOI: https://doi.org/10.1016/S0165-0114(86)80034-3

[2] Y. Huang, BCI-algebra, Science Press, Beijing (2006).

[3] Y. Jun, K. Hur, K. Lee, Hyperfuzzy subalgebras of BCK=BCI-algebras, Annals of Fuzzy Mathematics and Informatics (in press).

[4] Y. Jun, S. Kim, F. Smarandache, Interval neutrosophic sets with applications in BCK=BCI-algebras, submitted to New Mathematics and Natural Computation.

[5] J. Meng, Y. Jun, BCI-algebras, Kyungmoon Sa Co., Seoul (1994).

[6] F. Smarandache, Neutrosophy, Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA (1998), URL: http://fs.gallup.unm.edu/eBook-neutrosophics6.pdf last edition online.

[7] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Reserch Press, Rehoboth, NM (1999).

[8] F. Smarandache, Neutrosophic set – a generalization of the intuitionistic fuzzy set, International Journal of Pure and Applied Mathematics, vol. 24(3) (2005), pp. 287–297.

[9] H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, no. 5 in Neutrosophic Book Series, Hexis (2005).

[10] H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, no. 5 in Neutrosophic Book Series, Hexis, Phoenix, Ariz, USA (2005), DOI: http://dx.doi.org/10.6084/m9.figshare.6199013.v1

[11] H. Wang, Y. Zhang, R. Sunderraman, Truth-value based interval neutrosophic sets, [in:] 2005 IEEE International on Conference Granular Computing, vol. 1 (2005), pp. 274–277, DOI: http://dx.doi.org/10.1109/GRC.2005.1547284 DOI: https://doi.org/10.1109/GRC.2005.1547284