Volume 21 • Issue 2 • PP: 84-97 • 2023
MBJ-Neutrosophic Positive Implicative LI-ideals, Associative LI-ideals, and Fantastic LI-ideals
Open Access & Copyright
© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF 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
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.
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.