Volume 18 , Issue 4 , PP: 223-237, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
Aiyared Iampan 1 * , P. Jayaraman 2 , S. D. Sudha 3 , N. Rajesh 4
Doi: https://doi.org/10.54216/IJNS.180420
The concept of interval-valued neutrosophic sets (IVNSs) was first introduced by Wang et al. (Wang, H.;
Smarandache, F.; Zhang, Y. Q.; Sunderraman, R. Interval neutrosophic sets and logic: Theory and applications
in computing. Hexis, Phoenix, Ariz, USA, 2005.). In this paper, the concept of IVNSs to ideals of Hilbert
algebras is introduced. The homomorphic inverse image of interval-valued neutrosophic ideals (IVN ideals)
in Hilbert algebras is also studied and some related properties are investigated.
Hilbert algebra , ideal , interval-valued neutrosophic ideal , level cut
[1] Ahmad B.; Kharal, A. On fuzzy soft sets. Adv. Fuzzy Syst. 2009, 2009, Article ID 586507, 6 pages.
[2] Atanassov, K. T. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986, 20(1), 87–96.
[3] Atef, M.; Ali, M. I.; Al-shami, T. Fuzzy soft covering based multi-granulation fuzzy rough sets and their
applications. Comput. Appl. Math. 2021, 40(4), 115.
[4] Busneag, D. A note on deductive systems of a Hilbert algebra. Kobe J. Math. 1985, 2, 29–35.
[5] Busneag, D. Hilbert algebras of fractions and maximal Hilbert algebras of quotients. Kobe J. Math.
1988, 5, 161–172.
[6] Caˇgman, N.; Enginoˇglu, S.; Citak, F. Fuzzy soft set theory and its application. Iran. J. Fuzzy Syst. 2011,
8(3), 137–147.
[7] Chajda, I.; Halas, R. Congruences and ideals in Hilbert algebras. Kyungpook Math. J. 1999, 39(2),
429–429.
[8] Diego, A. Sur les alg´ebres de Hilbert. Collection de Logique Math. Ser. A (Ed. Hermann, Paris) 1966,
21, 1–52.
[9] Dudek, W. A. On fuzzification in Hilbert algebras. Contrib. Gen. Algebra 1999, 11, 77–83.
[10] Dudek, W. A.; Jun, Y. B. On fuzzy ideals in Hilbert algebra. Novi Sad J. Math. 1999, 29(2), 193–207.
[11] Garg, H.; Kumar, K. An advanced study on the similarity measures of intuitionistic fuzzy sets based
on the set pair analysis theory and their application in decision making. Soft Comput. 2018, 22(15),
4959–4970.
[12] Garg, H.; Kumar, K. Distance measures for connection number sets based on set pair analysis and its
applications to decision-making process. Appl. Intell. 2018, 48(10), 3346–3359.
[13] Garg, H.; Singh, S. A novel triangular interval type-2 intuitionistic fuzzy set and their aggregation
operators. Iran. J. Fuzzy Syst. 2018, 15(5), 69–93.
[14] Iampan, A.; Jayaraman, P.; Sudha, S. D.; Rajesh, N. Interval-valued neutrosophic subalgebras of Hilbert
algebras. (submitted).
[15] Jun, Y. B. Deductive systems of Hilbert algebras. Math. Japon. 1996, 43, 51–54.
[16] Jun, Y. B.; Smarandache, F.; Kim, C. S. Neutrosophic cubic sets. New Math. Nat. Comput. 2017, 13(1),
41–54.
[17] Smarandache, F. A unifying field in logics: Neutrosophic logic, neutrosophy, neutrosophic set, neutrosophic
probability. American Research Press, 1999.
[18] Smarandache, F. Neutrosophic set, a generalization of intuitionistic fuzzy sets. Int. J. Pure Appl. Math.
2005, 24(5), 287–297.
[19] Taboon, K.; Butsri, P.; Iampan, A. A cubic set theory approach to UP-algebras. J. Interdiscip. Math.
2020, 23(8), 1449–1486.
[20] Wang, H.; Smarandache, F.; Zhang, Y. Q.; Sunderraman, R. Interval neutrosophic sets and logic: Theory
and applications in computing. Hexis, Phoenix, Ariz, USA, 2005.
[21] Zadeh, L. A. Fuzzy sets. Inf. Control 1965, 8(3), 338–353.
