1
Department of Mathematics, Acharya Nagarjuna universtiy, Guntur Dist., A.P, India
(vamarendrababu@anu.ac.in)
2
Department of H & S, KRUCET, Krishna university, Machilipatnam, A.P, India
(kruteacher211@kru.ac.in)
3
PVP Siddhartha institute of Technology, Vijayawada, A.P, India
(malleswari.v@pvpsiddhartha.ac.in)
Abstract :
The MBJ-Neutrosophic positive implicative LI-ideals, the MBJ-Neutrosophic associative LI-ideals, and the MBJ-Neutrosophic fantastic LI-ideals are all introduced in this study. Of all these ideals, several their qualities and corresponding conditions were explored. We have demonstrated how every positive implicative MBJ-Neutrosophic LI-ideal evolved into an MBJ-Neutrosophic LI-ideal, MBJ-Neutrosophic implicative LI-ideal, and MBJ-Neutrosophic fantastic LI-ideal. Additionally, it was demonstrated that any MBJ-Neutrosophic fantastic LI-ideal is a MBJ-Neutrosophic associative LI-ideal.
Keywords :
Lattice implication algebra (LIA); MBJ-Neutrosophic LI-ideal (MBJ-NLII) , MBJ-Neutrosophic implicative LI-ideal (MBJ-NILII) , MBJ-Neutrosophic positive implicative LI-ideal (MBJ-NPILII) , MBJ-Neutrosophic associative LI-ideal (MBJ-NALII) , and MBJ-Neutrosophic fantastic LI-ideal (MBJ-NFLII) .
References :
[1] Amarendra Babu. V, Abida Begum. K* and Siva Naga Malleswari. V on “MBJ-Neutrosophic LI-Ideals in Lattice Implication Algebras” published in Journal of Stochastic Modeling & Applications, ISSN: 0972-3641, Vol. 26 No. 3, page no.791-804, (January-June, Special Issues 2022 part-6).
[2] Amarendra Babu. V, Abida Begum. K* and Siva Naga Malleswari. V on “MBJ-Neutrosophic Implicative LI-Ideals in Lattice Implication Algebras” published in Mathematical Statistician and Engineering Applications, ISSN: 2094-0343, 2326-9865, Vol.71, No. 3s2 (2022), page nos. 1022 - 1031.http://philstat.org.ph.
[3] Borzooei R.A., Sabetkish M., and Jun Y.B., Neutrosophic LΙ-Ideal in lattice implication algebras, Neutrosophic Sets and Systems 31, 1 (2020). http://digitalrepository.unm.edu/ nss_journal/vol/31/iss1/20.
[4] Borzooei R.A., Zhang X.H., Smarandache F. and Jun Y.B., Commutative\generalized Neutrosophic ideals in BCK-algebras, Symmetry 10 (2018), 350 doi: 10.3390/sym10080350. Google Scholar.
[5] Jun Y.B., Roh E.H. and Xu Y., LI-ideals in lattice implication algebras, Bull. Korean Math. Soc. 35(1) (1998), 13–24.Google Scholar.
[6] Jun Y.B., Kim S.J. and Smarandache F., Interval Neutrosophic sets with Applications in BCK/BCI-algebra, Axioms 7 (2018), 23. doi: 10.3390/axioms7020023. Google Scholar.
[7] Jun Y.B., Smarandache F. and Bordbar H., Neutrosophic N-structures applied to BCK/BCI-algebras, Information 8 (2017), 128. doi: 10.3390/info8040128. Google Scholar.
[8] Jun Y.B., Smarandache F., Song S.Z. and Khan M., Neutrosophic positive Implicative N-Ideals in BCK/BCI-algebras, Axioms 7 (2018), 3. doi: 10.3390/axioms7010003. Google Scholar.
[9] Jun Y.B. , E.H. Roh and Xu. Y, LΙ-Ideals in Lattice implication algebras, Bulletin of the Korean Mathematical Society, 35(1) (1998), 13–24.
[10] Jun. Y.B, S. J. Kim and F. Smarandache, Interval Neutrosophic sets with applications in BCK / BCI algebra, Axioms 2018, 7, 23; doi:10.3390/axioms 7020023.
[11] Mohseni Takallo. M, R. A. Borzooei, Young Bae Jun, MBJ-Neutrosophic structures andits applications in BCK/BCI-algebras, Neutrosophic sets and systems,Vol 23,72-84,2018.
[12] Ozturk M.A. and Jun Y.B., Neutrosophic ideals in BCK/BCI-algebras based on Neutrosophic points, J. Inter. Math. Virtual Inst. 8 (2018), 1–17.Google Scholar.
[13] Smarandache F., Neutrosophic set, a generalization of intuitionistic fuzzy sets, International Journal of Pure and Applied Mathematics 24(5) (2005), 287–297. Google Scholar.
[14] Smarandache. F, A Unifying Field in Logics: Neutrosophic Logic, in Multiple Valued Logic / An International Journal, Vol. 8, No. 3, 385-438, 2002, www.gallup.unm.edu /~smarandache/eBook-neutrosophics4.pdf.
[15] Smarandache. F, Definition of Neutrosophic Logic – A Generalization of the Intuitionistic Fuzzy Logic, Proceedings of the Third Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2003, September 10-12, 2003, Zittau, Germany; University of Applied Sciences at Zittau/Goerlitz, 141-146.
[16] Smarandache. F, Introduction to Neutrosophic Statistics, Sitech, 2014, http://fs. gallup. unm.edu/NeutrosophicStatistics.pdf,2014.
[17] Song S.Z., Smarandache. F., and Jun Y.B., Neutrosophic commutative N-Ideals in BCK-algebras, Information 8 (2017), 130. doi: 10.3390/info8040130. Google Scholar.
[18] Xu Y., Lattice implication algebras, J. Southwest Jiaotong Univ. 1 (1993), 20–27. Google Scholar.
| Style | # |
|---|---|
| MLA | Amarendra Babu V., Abida Begum K., Siva Naga Malleswari V.. "MBJ-Neutrosophic Positive Implicative LI-ideals, Associative LI-ideals, and Fantastic LI-ideals." International Journal of Neutrosophic Science, Vol. 21, No. 2, 2023 ,PP. 84-97 (Doi : https://doi.org/10.54216/IJNS.210208) |
| APA | Amarendra Babu V., Abida Begum K., Siva Naga Malleswari V.. (2023). MBJ-Neutrosophic Positive Implicative LI-ideals, Associative LI-ideals, and Fantastic LI-ideals. Journal of International Journal of Neutrosophic Science, 21 ( 2 ), 84-97 (Doi : https://doi.org/10.54216/IJNS.210208) |
| Chicago | Amarendra Babu V., Abida Begum K., Siva Naga Malleswari V.. "MBJ-Neutrosophic Positive Implicative LI-ideals, Associative LI-ideals, and Fantastic LI-ideals." Journal of International Journal of Neutrosophic Science, 21 no. 2 (2023): 84-97 (Doi : https://doi.org/10.54216/IJNS.210208) |
| Harvard | Amarendra Babu V., Abida Begum K., Siva Naga Malleswari V.. (2023). MBJ-Neutrosophic Positive Implicative LI-ideals, Associative LI-ideals, and Fantastic LI-ideals. Journal of International Journal of Neutrosophic Science, 21 ( 2 ), 84-97 (Doi : https://doi.org/10.54216/IJNS.210208) |
| Vancouver | Amarendra Babu V., Abida Begum K., Siva Naga Malleswari V.. MBJ-Neutrosophic Positive Implicative LI-ideals, Associative LI-ideals, and Fantastic LI-ideals. Journal of International Journal of Neutrosophic Science, (2023); 21 ( 2 ): 84-97 (Doi : https://doi.org/10.54216/IJNS.210208) |
| IEEE | Amarendra Babu V., Abida Begum K., Siva Naga Malleswari V., MBJ-Neutrosophic Positive Implicative LI-ideals, Associative LI-ideals, and Fantastic LI-ideals, Journal of International Journal of Neutrosophic Science, Vol. 21 , No. 2 , (2023) : 84-97 (Doi : https://doi.org/10.54216/IJNS.210208) |