1
Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand
(aiyared.ia@up.ac.th)
2
Department of Mathematics, Bharathiyar University, Coimbatore-641046, Tamilnadu, India
(jrmsathya@gmail.com)
3
Department of Mathematics, Bharathiyar University, Coimbatore-641046, Tamilnadu, India
(sudhaa88@gmail.com)
4
Laboratory of Information Processing, Faculty of Science Ben M’Sik, Universit´s Hassan II, BP 7955 Casablanca, Morocco
(broumisaid78@gmail.com)
5
Department of Mathematics, Rajah Serfoji Government College, Thanjavur-613005, Tamilnadu, India
(nrajesh topology@yahoo.co.in)
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.10–12 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 :
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[13] Y. B. Jun, Deductive systems of Hilbert algebras, Math. Japon., vol. 43, pp. 51–54, 1996.
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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.
| Style | # |
|---|---|
| MLA | Aiyared Iampan, P. Jayaraman, S. D. Sudha, Said Broumi, N. Rajesh. "Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras." International Journal of Neutrosophic Science, Vol. 19, No. 1, 2022 ,PP. 363-374 (Doi : https://doi.org/10.54216/IJNS.190133) |
| APA | Aiyared Iampan, P. Jayaraman, S. D. Sudha, Said Broumi, N. Rajesh. (2022). Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras. Journal of International Journal of Neutrosophic Science, 19 ( 1 ), 363-374 (Doi : https://doi.org/10.54216/IJNS.190133) |
| Chicago | Aiyared Iampan, P. Jayaraman, S. D. Sudha, Said Broumi, N. Rajesh. "Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras." Journal of International Journal of Neutrosophic Science, 19 no. 1 (2022): 363-374 (Doi : https://doi.org/10.54216/IJNS.190133) |
| Harvard | Aiyared Iampan, P. Jayaraman, S. D. Sudha, Said Broumi, N. Rajesh. (2022). Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras. Journal of International Journal of Neutrosophic Science, 19 ( 1 ), 363-374 (Doi : https://doi.org/10.54216/IJNS.190133) |
| Vancouver | Aiyared Iampan, P. Jayaraman, S. D. Sudha, Said Broumi, N. Rajesh. Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras. Journal of International Journal of Neutrosophic Science, (2022); 19 ( 1 ): 363-374 (Doi : https://doi.org/10.54216/IJNS.190133) |
| IEEE | Aiyared Iampan, P. Jayaraman, S. D. Sudha, Said Broumi, N. Rajesh, Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras, Journal of International Journal of Neutrosophic Science, Vol. 19 , No. 1 , (2022) : 363-374 (Doi : https://doi.org/10.54216/IJNS.190133) |