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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 19Issue 1PP: 363-374 • 2022

Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras

Aiyared Iampan 1* ,
P. Jayaraman 2 ,
S. D. Sudha 2 ,
Said Broumi 3 ,
N. Rajesh 4
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
3Laboratory of Information Processing, Faculty of Science Ben M’Sik, Universit´s Hassan II, BP 7955 Casablanca, Morocco
4Department of Mathematics, Rajah Serfoji Government College, Thanjavur-613005, Tamilnadu, India
* Corresponding Author.
Received: March 07, 2022 Accepted: September 13, 2022

Abstract

Interval-valued neutrosophic sets (IVNSs) are a notion that was initially developed by Wang et al.19 The idea

of IVNSs to deductive systems (DSs) in Hilbert algebras is presented in this study. It is shown how intervalvalued

neutrosophic deductive systems (IVNDSs) relate to their level cuts. In addition, certain related features

are examined as well as the homomorphic inverse image of IVNDSs in Hilbert algebras.

Keywords

Zadeh20 first developed the idea of fuzzy sets (FSs). Numerous academics have studied FS theory because it has numerous practical applications. Numerous investigations were undertaken on the generalizations of FSs after the idea of FSs was introduced. In 1 3 6 it is explained how FSs may be integrated with various uncertainty-reduction strategies like soft sets and rough sets. The idea of intuitionistic fuzzy sets (IFSs) as out by Atanassov 2 is one of the more beneficial extensions of FSs. Medical diagnostics optimization problems and multi-criteria decision-making are just a few of the areas in which IFSs are applied.10&ndash 12 In 1999 Smarandache16 presented the idea of neutrosophic sets which is a broader concept that encompasses the ideas of classic sets FSs IFSs and interval-valued (I)FSs (see16 17).

References

[1] B. Ahmad, A. Kharal, On fuzzy soft sets, Adv. Fuzzy Syst., vol. 2009, Article ID 586507, 6 pages, 2009.

[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., vol. 20, no. 1, pp. 87–96, 1986.

[3] M. Atef, M. I. Ali, T. Al-shami, Fuzzy soft covering based multi-granulation fuzzy rough sets and their

applications, Comput. Appl. Math., vol. 40, no. 4, pp. 115, 2021.

[4] D. Busneag, A note on deductive systems of a Hilbert algebra, Kobe J. Math., vol. 2, pp. 29–35, 1985.

[5] D. Busneag, Hilbert algebras of fractions and maximal Hilbert algebras of quotients, Kobe J. Math., vol.

5, pp. 161–172, 1988.

[6] N. Caˇgman, S. Enginoˇglu, F. Citak, Fuzzy soft set theory and its application, Iran. J. Fuzzy Syst., vol. 8,

no. 3, pp. 137–147, 2011.

[7] A. Diego, Sur les alg´ebres de Hilbert, Collection de Logique Math. Ser. A (Ed. Hermann, Paris), vol. 21,

pp. 1–52, 1966.

[8] W. A. Dudek, On fuzzification in Hilbert algebras, Contrib. Gen. Algebra, vol. 11, pp. 77–83, 1999.

[9] W. A. Dudek, On ideals in Hilbert algebras, Acta Universitatis Palackianae Olomuciensis Fac. rer. nat.

ser. Math., vol. 38, pp. 31–34, 1999.

[10] H. Garg, K. Kumar, 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., vol. 22, no. 15, pp.

4959–4970, 2018.

[11] H. Garg, K. Kumar, Distance measures for connection number sets based on set pair analysis and its

applications to decision-making process, Appl. Intell., vol. 48, no. 10, pp. 3346–3359, 2018.

[12] H. Garg, S. Singh, A novel triangular interval type-2 intuitionistic fuzzy set and their aggregation operators,

Iran. J. Fuzzy Syst., vol. 15, no. 5, pp. 69–93, 2018.

[13] Y. B. Jun, Deductive systems of Hilbert algebras, Math. Japon., vol. 43, pp. 51–54, 1996.

[14] Y. B. Jun, R. Bandaru, Deductive systems of GE-algebras, Algebr. Struct. Appl., vol. 9, no. 1, pp. 53–67,

2022.

[15] Y. B. Jun, F. Smarandache, C. S. Kim, Neutrosophic cubic sets, New Math. Nat. Comput., vol. 13, no. 1,

pp. 41–54, 2017.

[16] F. Smarandache, A unifying field in logics: Neutrosophic logic, neutrosophy, neutrosophic set, neutrosophic

probability, American Research Press, 1999.

[17] F. Smarandache, Neutrosophic set, a generalization of intuitionistic fuzzy sets, Int. J. Pure Appl. Math.,

vol. 24, no. 5, pp. 287–297, 2005.

[18] K. Taboon, P. Butsri, A. Iampan, A cubic set theory approach to UP-algebras, J. Interdiscip. Math., vol.

23, no. 8, pp. 1449–1486, 2020.

[19] H. Wang, F. Smarandache, Y. Q. Zhang, R. Sunderraman, Interval neutrosophic sets and logic: Theory

and applications in computing, Hexis, Phoenix, Ariz, USA, 2005.

[20] L. A. Zadeh, Fuzzy sets, Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.

[21] J. Zhan, Z. Tan, Intuitionistic fuzzy deductive systems in Hibert algebra, Southeast Asian Bull. Math.,

vol. 29, no. 4, pp. 813–826, 2005.

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Iampan, Aiyared, Jayaraman, P., Sudha, S. D., Broumi, Said, Rajesh, N.. "Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras." International Journal of Neutrosophic Science, vol. Volume 19, no. Issue 1, 2022, pp. 363-374. DOI: https://doi.org/10.54216/IJNS.190133
Iampan, A., Jayaraman, P., Sudha, S., Broumi, S., Rajesh, N. (2022). Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras. International Journal of Neutrosophic Science, Volume 19(Issue 1), 363-374. DOI: https://doi.org/10.54216/IJNS.190133
Iampan, Aiyared, Jayaraman, P., Sudha, S. D., Broumi, Said, Rajesh, N.. "Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras." International Journal of Neutrosophic Science Volume 19, no. Issue 1 (2022): 363-374. DOI: https://doi.org/10.54216/IJNS.190133
Iampan, A., Jayaraman, P., Sudha, S., Broumi, S., Rajesh, N. (2022) 'Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras', International Journal of Neutrosophic Science, Volume 19(Issue 1), pp. 363-374. DOI: https://doi.org/10.54216/IJNS.190133
Iampan A, Jayaraman P, Sudha S, Broumi S, Rajesh N. Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras. International Journal of Neutrosophic Science. 2022;Volume 19(Issue 1):363-374. DOI: https://doi.org/10.54216/IJNS.190133
A. Iampan, P. Jayaraman, S. Sudha, S. Broumi, N. Rajesh, "Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras," International Journal of Neutrosophic Science, vol. Volume 19, no. Issue 1, pp. 363-374, 2022. DOI: https://doi.org/10.54216/IJNS.190133
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