1
Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar,Guntur-522 510,Andhra Pradesh,India
(drbsn63@yahoo.co.in)
2
Department of Mathematics, Sir C.R.Reddy College of Engineering,Eluru-534007,Andhra Pradesh,India
(shakebaji6@gmail.com)
3
Department Of Engineering Mathematics,College of Engineering,Koneru Lakshmaih Educational Fondation,Vaddeswaram-522302,Guntur(DT),Andhra Pradesh,India
(ram.fuzzy@gmail.com)
4
Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, B.P 7955, Morocco
(broumisaid78@gmail.com)
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.
| Style | # |
|---|---|
| MLA | B. Satyanarayana, Shake Baji, D. Ramesh, Said Broumi. "Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra." International Journal of Neutrosophic Science, Vol. 22, No. 1, 2023 ,PP. 45-59 (Doi : https://doi.org/10.54216/IJNS.220104) |
| APA | B. Satyanarayana, Shake Baji, D. Ramesh, Said Broumi. (2023). Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra. Journal of International Journal of Neutrosophic Science, 22 ( 1 ), 45-59 (Doi : https://doi.org/10.54216/IJNS.220104) |
| Chicago | B. Satyanarayana, Shake Baji, D. Ramesh, Said Broumi. "Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra." Journal of International Journal of Neutrosophic Science, 22 no. 1 (2023): 45-59 (Doi : https://doi.org/10.54216/IJNS.220104) |
| Harvard | B. Satyanarayana, Shake Baji, D. Ramesh, Said Broumi. (2023). Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra. Journal of International Journal of Neutrosophic Science, 22 ( 1 ), 45-59 (Doi : https://doi.org/10.54216/IJNS.220104) |
| Vancouver | B. Satyanarayana, Shake Baji, D. Ramesh, Said Broumi. Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra. Journal of International Journal of Neutrosophic Science, (2023); 22 ( 1 ): 45-59 (Doi : https://doi.org/10.54216/IJNS.220104) |
| IEEE | B. Satyanarayana, Shake Baji, D. Ramesh, Said Broumi, Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra, Journal of International Journal of Neutrosophic Science, Vol. 22 , No. 1 , (2023) : 45-59 (Doi : https://doi.org/10.54216/IJNS.220104) |