ASPG Menu
search

American Scientific Publishing Group

verified Journal

International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
Frequency

Continuous publication

Publication Model

Open access · Articles freely available online · APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Volume 18Issue 4PP: 223-237 • 2022

Interval-Valued Neutrosophic Ideals of Hilbert Algebras

Aiyared Iampan 1* ,
P. Jayaraman 2 ,
S. D. Sudha 2 ,
N. Rajesh 3
1Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand
2Department of Mathematics, Bharathiyar University, Coimbatore 641046, Tamilnadu, India
3Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, India
* Corresponding Author.
Received: March 19, 2022 Accepted: June 29, 2022

Abstract

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.

Keywords

Hilbert algebra ideal interval-valued neutrosophic ideal level cut

References

[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.

Cite This Article

Choose your preferred format

format_quote
Iampan, Aiyared, Jayaraman, P., Sudha, S. D., Rajesh, N.. "Interval-Valued Neutrosophic Ideals of Hilbert Algebras." International Journal of Neutrosophic Science, vol. Volume 18, no. Issue 4, 2022, pp. 223-237. DOI: https://doi.org/10.54216/IJNS.180420
Iampan, A., Jayaraman, P., Sudha, S., Rajesh, N. (2022). Interval-Valued Neutrosophic Ideals of Hilbert Algebras. International Journal of Neutrosophic Science, Volume 18(Issue 4), 223-237. DOI: https://doi.org/10.54216/IJNS.180420
Iampan, Aiyared, Jayaraman, P., Sudha, S. D., Rajesh, N.. "Interval-Valued Neutrosophic Ideals of Hilbert Algebras." International Journal of Neutrosophic Science Volume 18, no. Issue 4 (2022): 223-237. DOI: https://doi.org/10.54216/IJNS.180420
Iampan, A., Jayaraman, P., Sudha, S., Rajesh, N. (2022) 'Interval-Valued Neutrosophic Ideals of Hilbert Algebras', International Journal of Neutrosophic Science, Volume 18(Issue 4), pp. 223-237. DOI: https://doi.org/10.54216/IJNS.180420
Iampan A, Jayaraman P, Sudha S, Rajesh N. Interval-Valued Neutrosophic Ideals of Hilbert Algebras. International Journal of Neutrosophic Science. 2022;Volume 18(Issue 4):223-237. DOI: https://doi.org/10.54216/IJNS.180420
A. Iampan, P. Jayaraman, S. Sudha, N. Rajesh, "Interval-Valued Neutrosophic Ideals of Hilbert Algebras," International Journal of Neutrosophic Science, vol. Volume 18, no. Issue 4, pp. 223-237, 2022. DOI: https://doi.org/10.54216/IJNS.180420
Digital Archive Ready