Volume 23 , Issue 4 , PP: 358-368, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Aiyared Iampan 1 * , N. Rajesh 2
Doi: https://doi.org/10.54216/IJNS.230429
The notion of neutrosophic N-deductive systems of Hilbert algebras is introduced, and several properties are investigated. Conditions for neutrosophic N-structures to be neutrosophic N-deductive systems of Hilbert algebras are provided. Relations between neutrosophic N-deductive systems and their level subsets are considered. The Cartesian product of neutrosophic N-structures is also supplied. Finally, we also find the property of the homomorphic pre-image of neutrosophic N-deductive systems.
Hilbert algebra , neutrosophic N-structure , neutrosophic N-deductive system , homomorphic pre-image.
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1), (1986), 87-96.
[2] D. Busneag, A note on deductive systems of a Hilbert algebra, Kobe J. Math., 2, (1985), 29-35.
[3] D. Busneag, Hilbert algebras of fractions and maximal Hilbert algebras of quotients, Kobe J. Math., 5, (1988), 161-172.
[4] I. Chajda and R. Halas, Congruences and ideals in Hilbert algebras, Kyungpook Math. J., 39(2), (1999), 429-429.
[5] A. Diego, Sur les alg´ebres de Hilbert, Collection de Logique Math. Ser. A (Ed. Hermann, Paris), 21, (1966), 1-52.
[6] W. A. Dudek, On fuzzification in Hilbert algebras, Contrib. Gen. Algebra, 11, (1999), 77-83.
[7] W. A. Dudek, On ideals in Hilbert algebras, Acta Universitatis Palackianae Olomuciensis Fac. rer. nat. ser. Math., 38, (1999), 31-34.
[8] W. A. Dudek and Y. B. Jun, On fuzzy ideals in Hilbert algebra, Novi Sad J. Math., 29(2), (1999), 193-207.
[9] L. Henkin, An algebraic characterization of quantifiers, Fund. Math., 37, (1950), 63-74.
[10] A. Iampan and N. Rajesh, Neutrosophic N-structures over Hilbert algebras, Int. J. Neutrosophic Sci., 23(3), (2024), 208-219.
[11] Y. B. Jun, Deductive systems of Hilbert algebras, Math. Japon., 43, (1996), 51-54.
[12] Y. B. Jun, K. Lee, and S.-Z. Song, N-ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc., 22, (2009), 417-437.
[13] Y. B. Jun, F. Smarandache, and H. Bordbar, Neutrosophic N-structures applied to BCK/BCI-algebras, Information, 8, (2017), 128.
[14] Y. B. Jun, F. Smarandache, S.-Z. Song, and M. Khan, Neutrosophic positive implicative N-ideals in BCK-algebras, Axioms, 7(1), (2018), 3.
[15] M. Khan, S. Anis, F. Smarandache, and Y. B. Jun, Neutrosophic N-structures and their applications in semigroups, Ann. Fuzzy Math. Inform., 14(6), (2017), 583-598.
[16] P. Rangsuk, P. Huana, and A. Iampan, Neutrosophic N-structures over UP-algebras, Neutrosophic Sets Syst., 28, (2019), 87-127.
[17] F. Smarandache, A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability (fourth edition), Rehoboth American Research Press, 2008.
[18] F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24(3), (2005), 287-297.
[19] S.-Z. Song, F. Smarandache, and Y. B. Jun, Neutrosophic commutative N-ideals in BCK-algebras, Information, 8, (2017), 130.
[20] L. A. Zadeh, Fuzzy sets, Inf. Control, 8(3), (1965), 338-353.
