Length Neutrosophic Subalgebras of BCK=BCI-Algebras

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

Bulletin of the Section of Logic (2020)

  • Volume: 49, Issue: 4, page 377-400
  • ISSN: 0138-0680

Abstract

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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.

How to cite

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Young Bae Jun, et al. "Length Neutrosophic Subalgebras of BCK=BCI-Algebras." Bulletin of the Section of Logic 49.4 (2020): 377-400. <http://eudml.org/doc/296795>.

@article{YoungBaeJun2020,
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.},
author = {Young Bae Jun, Madad Khan, Florentin Smarandache, Seok-Zun Song},
journal = {Bulletin of the Section of Logic},
keywords = {interval neutrosophic set; interval neutrosophic length; length neutrosophic subalgebra},
language = {eng},
number = {4},
pages = {377-400},
title = {Length Neutrosophic Subalgebras of BCK=BCI-Algebras},
url = {http://eudml.org/doc/296795},
volume = {49},
year = {2020},
}

TY - JOUR
AU - Young Bae Jun
AU - Madad Khan
AU - Florentin Smarandache
AU - Seok-Zun Song
TI - Length Neutrosophic Subalgebras of BCK=BCI-Algebras
JO - Bulletin of the Section of Logic
PY - 2020
VL - 49
IS - 4
SP - 377
EP - 400
AB - 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.
LA - eng
KW - interval neutrosophic set; interval neutrosophic length; length neutrosophic subalgebra
UR - http://eudml.org/doc/296795
ER -

References

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  1. [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 
  2. [2] Y. Huang, BCI-algebra, Science Press, Beijing (2006). 
  3. [3] Y. Jun, K. Hur, K. Lee, Hyperfuzzy subalgebras of BCK=BCI-algebras, Annals of Fuzzy Mathematics and Informatics (in press). 
  4. [4] Y. Jun, S. Kim, F. Smarandache, Interval neutrosophic sets with applications in BCK=BCI-algebras, submitted to New Mathematics and Natural Computation. 
  5. [5] J. Meng, Y. Jun, BCI-algebras, Kyungmoon Sa Co., Seoul (1994). 
  6. [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. [7] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Reserch Press, Rehoboth, NM (1999). 
  8. [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. [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. [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. [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 

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