ASPG Menu
search

American Scientific Publishing Group

verified Journal

International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
Frequency

Continuous publication

Publication Model

Open access · Articles freely available online · APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Volume 22Issue 1PP: 45-59 • 2023

Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra

B. Satyanarayana 1* ,
Shake Baji 2 ,
D. Ramesh 3 ,
Said Broumi 4
1Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar,Guntur-522 510,Andhra Pradesh,India
2Department of Mathematics, Sir C.R.Reddy College of Engineering,Eluru-534007,Andhra Pradesh,India
3Department Of Engineering Mathematics,College of Engineering,Koneru Lakshmaih Educational Fondation,Vaddeswaram-522302,Guntur(DT),Andhra Pradesh,India
4Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, B.P 7955, Morocco
* Corresponding Author.
Received: March 28, 2023 Revised: June 19, 2023 Accepted: August 24, 2023

Abstract

The notion of Positive Implicative BS-Neutrosophic Ideal, Commutative BS-Neutrosophic Ideal and related properties are investigated. Characterizations of Positive Implicative BS-Neutrosophic Ideal, Commutative BS- Neutrosophic Ideal are discussed.

Keywords

BS-Neutrosophic Set (BS-NSS) BS- Neutrosophic Ideal (BS-NSI) Positive Implicative BSNeutrosophic Ideal (PI BS-NSI) Commutative BS-Neutrosophic Ideal (C BS-NSI).

References

[1] L. A. Zadeh, “Fuzzy sets,” Inf. Control, vol. 8, pp. 338–353, 1965. https://doi.org/10.1016/ S0019-9958(65)90241-X

[2] K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets Syst., vol. 20, no. 1, pp. 87–96, 1986, doi: https://doi.org/10.1016/S0165-011480034-3.

[3] F. Smarandache, “Neutrosophic set - a generalization of the intuitionistic fuzzy set,” in 2006 IEEE International Conference on Granular Computing, 2006, pp. 38–42. https://doi.org/10.1109/ GRC.2006.1635754

[4] F. Smarandache, “A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (fourth edition)”.

[5] M. M. Takallo, R. A. Borzooei, and Y. B. Jun, “MBJ-neutrosophic structures and its applications in BCK/BCI-algebras,” Neutrosophic Sets Syst., vol. 23, no. December, pp. 72–84, 2018, https:// doi.org/10.5281/zenodo.2155212.

[6] R. Borzooei, X. Zhang, F. Smarandache, and Y. Jun, “Commutative Generalized Neutrosophic Ideals in BCK-Algebras,” Symmetry (Basel)., vol. 10, no. 8, p. 350, Aug. 2018, https://doi.org/10. 3390/sym10080350

[7] M. Sa and B. C. K. Bci, “Neutrosophic subalgebras of several types in BCK/BCI -algebras,” vol. 14, no. 1, pp. 75–86, 2017.https://doi.org/10.30948/afmi.2017.14.1.75

[8] Y. Jun, S. Kim, and F. Smarandache, “Interval Neutrosophic Sets with Applications in BCK/BCI-Algebra,” Axioms, vol. 7, no. 2, p. 23, Apr. 2018, https://doi.org/10.3390/ axioms7020023

[9] Y. Jun, F. Smarandache, and H. Bordbar, “Neutrosophic N-Structures Applied to BCK/BCI-Algebras,” Information, vol. 8, no. 4, p. 128, Oct. 2017, https://doi.org/10.3390/info8040128

[10] Y. Jun, F. Smarandache, S.-Z. Song, and M. Khan, “Neutrosophic Positive Implicative N -Ideals in BCKAlgebras,” Axioms, vol. 7, no. 1, p. 3, Jan. 2018, https://doi.org/10.3390/axioms7010003

[11] Khan, Madad, Saima Anis, Florentin Smarandache, and Young Bae Jun. ”Neutrosophic N-structures and their applications in semigroups.” Annals of Fuzzy Mathematics and Informatics 14, no. 6 (2017): 583-598.

[12] M. Al¨ı Ozt¨urk and Y. Bae Jun, “Neutrosophic Ideals in BCK/Bci-Algebras Based on Neutrosophic Points,” J. Int. Math. Virtual Inst. Issn, vol. 8, pp. 1–17, 2018, http://dx.doi.org/10.7251/ JIMVI1801001%7F%C3%96

[13] Saeid, A. Borumand, and Young Bae Jun. ”Neutrosophic subalgebras of BCK/BCI-algebras based on Neutrosophic points.” Annals of Fuzzy Mathematics and Informatics 14, no. 1 (2017): 87-97.

[14] Smarandache, Florentin, and Surapati Pramanik. New trends in neutrosophic theory and applications. Vol. 1. Infinite Study, 2016.

[15] S. Song, F. Smarandache, and Y. Jun, “Neutrosophic Commutative N -Ideals in BCK-Algebras,” Information, vol. 8, no. 4, p. 130, Oct. 2017, https://doi.org/10.3390/info8040130

[16] Shake Baji B.Satyanarayana and U. Bindu Madhavi, “BS-neutrosophic Structures in BCK/BCIAlgebras.,” (communicated).

[17] Y. S. Huang, BCI-algebra. Beijing: Science Press, 2006.

[18] K. Iseki, “On BCI-algebras,” Math. Semin. Notes 8, pp. 125–130, 1980.

[19] Jie, J. M., and Young Bae Jun. ”BCK-algebras.” Kyung Moon Sa Co., Seoul, Republic of Korea 199 1994.

[20] L. A. Zadeh, “The Concept of a linguistic variable and its applications to approximate reasoning-I,” Information.Sci Control, vol. 8, pp. 199–249, 1975.

Cite This Article

Choose your preferred format

format_quote
Satyanarayana, B., Baji, Shake, Ramesh, D., Broumi, Said. "Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra." International Journal of Neutrosophic Science, vol. Volume 22, no. Issue 1, 2023, pp. 45-59. DOI: https://doi.org/10.54216/IJNS.220104
Satyanarayana, B., Baji, S., Ramesh, D., Broumi, S. (2023). Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra. International Journal of Neutrosophic Science, Volume 22(Issue 1), 45-59. DOI: https://doi.org/10.54216/IJNS.220104
Satyanarayana, B., Baji, Shake, Ramesh, D., Broumi, Said. "Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra." International Journal of Neutrosophic Science Volume 22, no. Issue 1 (2023): 45-59. DOI: https://doi.org/10.54216/IJNS.220104
Satyanarayana, B., Baji, S., Ramesh, D., Broumi, S. (2023) 'Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra', International Journal of Neutrosophic Science, Volume 22(Issue 1), pp. 45-59. DOI: https://doi.org/10.54216/IJNS.220104
Satyanarayana B, Baji S, Ramesh D, Broumi S. Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra. International Journal of Neutrosophic Science. 2023;Volume 22(Issue 1):45-59. DOI: https://doi.org/10.54216/IJNS.220104
B. Satyanarayana, S. Baji, D. Ramesh, S. Broumi, "Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra," International Journal of Neutrosophic Science, vol. Volume 22, no. Issue 1, pp. 45-59, 2023. DOI: https://doi.org/10.54216/IJNS.220104
Digital Archive Ready