Innovative Perspective on Neutrosophic Cubic Z-Algebras

G. Nisha; P.; R.; P.; Aiyared

doi:https://doi.org/10.54216/IJNS.230307

Full Length Article

Volume 23 • Issue 3 • PP: 77-86 • 2024

Innovative Perspective on Neutrosophic Cubic Z-Algebras

G. Nisha Devi ^1*

mail

,

P. Hemavathi ¹

mail

,

R. Vinodkumar ²

mail

,

P. Muralikrishna ³

mail

,

Aiyared Iampan ⁴

mail

¹Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences (SIMATS), Chennai-602105, India

²Department of Mathematics, Prathyusha Engineering College (Autonomous), Thiruvallur-602025, India

³Department of Mathematics, Muthurangam Government Arts College, Vellore-632002, India

⁴Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.230307

format_quote Cite this article

Received: August 25, 2023 Revised: November 28, 2023 Accepted: January 24, 2024

View PDF open_in_new

Abstract

This study explores an innovative perspective on neutrosophic cubic Z-algebras, delving into the theoretical framework within mathematical structures. Through a comprehensive analysis, we uncover unique insights that contribute to the advancement of algebraic methodologies, particularly in handling uncertainties represented by neutrosophic elements. This work aims to present the idea of neutrosophic cubic sets in Z-algebras, as well as the usage of false membership function, truth, and indeterminacy in Z-algebras. Further, the results on -union, -intersection, -union, and -intersection of neutrosophic cubic Z-subalgebras are provided. This paper also discusses homomorphisms of Z-algebras and its associated characteristics.

Keywords

Z-algebra Z-subalgebra Cubic set Cubic Z-subalgebra Neutrosophic set Neutrosophic cubic set Neutrosophic cubic Z-subalgebra.

References

[1] A. Rezaei & F. Smarandache, The neutrosophic triplet of BI-algebras. Neutrosophic Sets and Systems, 33, 313-321, 2020.

[2] M. A. A. Ansari & M. Chandramouleeswaran, Fuzzy β-subalgebras of β-algebras. International Journal of Mathematical Sciences and Engineering Applications, 7(5), 239-249, 2013.

[3] H. Bordbar, M. Mohseni Takallo, R. A. Borzooei & Y. B. Jun, BMBJ-Neutrosophic subalgebra in BCI/BCK-algebras. Neutrosophic Sets and Systems, 31, 31-43, 2020.

[4] E. A. El-Hamd, H. M. Shamma, M. Saleh & I. El-Khodary, Neutrosophic logic theory and applications. Neutrosophic Sets and Systems, 41, 30-51, 2021.

[5] P. Hemavathi, P. Muralikrishna & K. Palanivel, On interval valued intuitionistic fuzzy β-subalgebras. Afrika Matematika, 29(1-2), 249-262, 2018.

[6] R. Iqbal, S. Zafar & M. S. Sardar, Neutrosophic cubic subalgebras and neutrosophic cubic closed ideals of B-algebras. Neutrosophic Sets and Systems, 14, 47-60, 2016.

[7] Y. B. Jun, C. S. Kim & K. O. Yang, Cubic sets. Annals of Fuzzy Mathematics and Informatics, 4(1), 83-98, 2012.

[8] Y. B. Jun, M. S. Kim & S. T. Jung, Cubic subgroups. Annals of Fuzzy Mathematics and Informatics, 2(1), 9-15, 2011.

[9] Y. B. Jun, F. Samarandache & C. S. Kim, Neutrosophic cubic sets. New Mathematics and Natural Computation, 3(1), 45-54, 2017.

[10] Y. B. Jun, F. Samarandache & C. S. Kim, Neutrosophic subalgebras of several types in BCK/BCI-algebras. Annals of Fuzzy Mathematics and Informatics, 14(1), 75-86, 2017.

[11] Y. B. Jun, S.-Z. Song & S. J. Kim, Cubic interval-valued intuitionistic fuzzy sets and their application in BCK/BCI-algebras. Axioms, 7(1), 7, 2018.

[12] J. Awolola, A note on the concept of α-level sets of neutrosophic set. Neutrosophic Sets and Systems, 31, 120-126, 2020.

[13] P. K. Maji, Neutrosophic soft set. Annals of Fuzzy Mathematics and Informatics, 5(1), 157-168, 2013.

[14] M. Khalid, F. Smarandache, N. A. Khalid & S. Broumi, Translative and multiplicative interpretation of neutrosophic cubic set. Neutrosophic Sets and Systems, 35, 299-339, 2020.

[15] M. Khalid & N. A. Khalid, T-MBJ Neutrosophic set under M-subalgebra. Neutrosophic Sets and Systems, 38, 423-438, 2020.

[16] M. Khalid, N. A. Khalid & S. Broumi, T-Neutrosophic cubic set on BF-algebra. Neutrosophic Sets and Systems, 31, 127-147, 2020.

[17] P. Muralikrishna, R. Vinodkumar & G. Palani, Some aspects on cubic fuzzy β-subalgebra of β-algebra. Journal of Physics: Conference Series, 1597, 012018, 2020.

[18] T. Nanthini & A. Pushpalatha, Interval valued neutrosophic topological spaces. Neutrosophic Sets and Systems, 32, 52-60, 2020.

[19] J. Neggers & H. S. Kim, On β-algebras. Mathematica Slovaca, 52(5), 517-530, 2002.

[20] P. Muralikrishna & S. Manokaran, MBJ-Neutrosophic β-ideal of β-algebra. Neutrosophic Sets and Systems, 35, 99-118, 2020.

[21] R. A. Borzooei, F. Smarandache & Y. B. Jun, Polarity of generalized neutrosophic subalgebras in BCK/BCI-algebras. Neutrosophic Sets and Systems, 32, 123-145, 2020.

[22] P. B. Remy & A. Francina Shalini, Neutrosophic vague binary BCK/BCI-algebra, Neutrosophic Sets and Systems, 38, 45-67, 2020.

[23] F. Smarandache, Neutrosophic set, a generalization of the intuitionistic fuzzy sets. International Journal of Pure and Applied Mathematics, 24, 287-297, 2005.

[24] L. A. Zadeh, Fuzzy sets. Information and Control, 8(3), 338-353, 1965.

Cite This Article

Choose your preferred format

format_quote

Devi, G. Nisha, Hemavathi, P., Vinodkumar, R., Muralikrishna, P., Iampan, Aiyared. "Innovative Perspective on Neutrosophic Cubic Z-Algebras." International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 3, 2024, pp. 77-86. DOI: https://doi.org/10.54216/IJNS.230307

Devi, G., Hemavathi, P., Vinodkumar, R., Muralikrishna, P., Iampan, A. (2024). Innovative Perspective on Neutrosophic Cubic Z-Algebras. International Journal of Neutrosophic Science, Volume 23(Issue 3), 77-86. DOI: https://doi.org/10.54216/IJNS.230307

Devi, G. Nisha, Hemavathi, P., Vinodkumar, R., Muralikrishna, P., Iampan, Aiyared. "Innovative Perspective on Neutrosophic Cubic Z-Algebras." International Journal of Neutrosophic Science Volume 23, no. Issue 3 (2024): 77-86. DOI: https://doi.org/10.54216/IJNS.230307

Devi, G., Hemavathi, P., Vinodkumar, R., Muralikrishna, P., Iampan, A. (2024) 'Innovative Perspective on Neutrosophic Cubic Z-Algebras', International Journal of Neutrosophic Science, Volume 23(Issue 3), pp. 77-86. DOI: https://doi.org/10.54216/IJNS.230307

Devi G, Hemavathi P, Vinodkumar R, Muralikrishna P, Iampan A. Innovative Perspective on Neutrosophic Cubic Z-Algebras. International Journal of Neutrosophic Science. 2024;Volume 23(Issue 3):77-86. DOI: https://doi.org/10.54216/IJNS.230307

G. Devi, P. Hemavathi, R. Vinodkumar, P. Muralikrishna, A. Iampan, "Innovative Perspective on Neutrosophic Cubic Z-Algebras," International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 3, pp. 77-86, 2024. DOI: https://doi.org/10.54216/IJNS.230307

Digital Archive Ready