Neutrosophic set theory applied to Hilbert algebras

Aiyared; N.; B.

doi:https://doi.org/10.54216/IJNS.210409

Full Length Article

Volume 21 • Issue 4 • PP: 84-93 • 2023

Neutrosophic set theory applied to Hilbert algebras

Aiyared Iampan ^1*

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,

N. Rajesh ²

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,

B. Brundha ³

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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, Rajah Serfoji Government College (affiliated to Bharathidasan University), Thanjavur-613005, Tamilnadu, India

³Department of Mathematics, Government Arts College for Women, Orathanadu-614625, Tamilnadu, India

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.210409

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https://doi.org/10.54216/IJNS.210409 Received: January 28, 2023 Revised: May

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Abstract

In this paper, the notions of neutrosophic subalgebras, neutrosophic ideals, and neutrosophic deductive systems of Hilbert algebras are introduced, and some related properties are investigated. Relations between the notions are given. Finally, we study the properties of homomorphism of Hilbert algebras.

Keywords

Hilbert algebra neutrosophic subalgebra neutrosophic ideal neutrosophic deductive system.

References

[1] A. Al-Masarwah, A. G. Ahmad, G. Muhiuddin, Doubt N-ideals theory in BCK-algebras based on Nstructures, Ann. Commun. Math., vol. 3, no. 1, pp. 54-62, 2020.

[2] M. A. Ansari, I. A. H. Masmali, Ternary semigroups in terms of bipolar (λ, δ)-fuzzy ideals, Int. J. Algebra, vol. 9, no. 10, pp. 475-486, 2015.

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

[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] I. Chajda, R. Halas, Congruences and ideals in Hilbert algebras, Kyungpook Math. J., vol. 39, no. 2, pp. 429-429, 1999.

[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] W. A. Dudek, Y. B. Jun, On fuzzy ideals in Hilbert algebra, Novi Sad J. Math., vol. 29, no. 2, pp. 193-207, 1999.

[11] A. Iampan, P. Jayaraman, S. D. Sudha, N. Rajesh, Interval-valued neutrosophic ideals of Hilbert algebras, Int. J. Neutrosophic Sci., vol. 18, no. 4, pp. 223-237, 2022.

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

[13] R. Mahapatra, S. Samanta, M. Pal, Applications of edge colouring of fuzzy graphs, Informatica, vol. 31, no. 2, pp. 313-330, 2020.

[14] R. Mahapatra, S. Samanta, M. Pal, Generalized neutrosophic planar graphs and its application, J. Appl. Math. Comput., vol. 65, pp. 693-712, 2021.

[15] R. Mahapatra, S. Samanta, T. Allahviranloo, M. Pal, Radio fuzzy graphs and assignment of frequency in radio stations, Comp. Appl. Math., vol. 38, pp. 117, 2019.

[16] R. Mahapatra, S. Samanta, M. Pal, L. Jeong-Gon, K. K. Shah, N. Usman, B. Robin Singh, Colouring of COVID-19 affected region based on fuzzy directed graphs, Computers, Materials, & Continua, vol. 61, no. 1, pp. 1219-1233, 2021.

[17] R. Mahapatra, S. Samanta, M. Pal, Q. Xin, Link prediction in social networks by neutrosophic graph, Int. J. Comput. Intell. Syst., vol. 13, no. 1, pp. 1699-1713, 2020.

[18] G. Muhiuddin, p-ideals of BCI-algebras based on neutrosophic N-structures, J. Intell. Fuzzy Syst., vol. 40, no. 1, pp. 1097-1105, 2021.

[19] G. Muhiuddin, A. Mahboob, Int-soft ideals over the soft sets in ordered semigroups, AIMS Math., vol. 5, no. 3, pp. 2412–2423, 2020.

[20] T. Oner, T. Katican, A. B. Saeid, Neutrosophic N-structures on Sheffer stroke Hilbert algebras, Neutrosophic Sets Syst., vol. 42, pp. 221-238, 2021.

[21] P. Rangsuk, P. Huana, A. Iampan, Neutrosophic N-structures over UP-algebras, Neutrosophic Sets Syst., vol. 28, pp. 87-127, 2019.

[22] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press, Rehoboth, NM. 1999.

[23] F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., vol. 24, no. 3, pp. 287-297, 2005.

[24] M. Songsaeng, K. P. Shum, R. Chinram, A. Iampan, Neutrosophic implicative UP-filters, neutrosophic comparative UP-filters, and neutrosophic shift UP-filters of UP-algebras, Neutrosophic Sets Syst., vol. 47, pp. 620-643, 2021.

[25] N. Yaqoob, M. A. Ansari, Bipolar (λ, δ)-fuzzy ideals in ternary semigroups, Int. J. Math. Anal., Ruse, vol. 7, no. 36, pp. 1775-1782, 2013.

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

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Iampan, Aiyared, Rajesh, N., Brundha, B.. "Neutrosophic set theory applied to Hilbert algebras." International Journal of Neutrosophic Science, vol. Volume 21, no. Issue 4, 2023, pp. 84-93. DOI: https://doi.org/10.54216/IJNS.210409

Iampan, A., Rajesh, N., Brundha, B. (2023). Neutrosophic set theory applied to Hilbert algebras. International Journal of Neutrosophic Science, Volume 21(Issue 4), 84-93. DOI: https://doi.org/10.54216/IJNS.210409

Iampan, Aiyared, Rajesh, N., Brundha, B.. "Neutrosophic set theory applied to Hilbert algebras." International Journal of Neutrosophic Science Volume 21, no. Issue 4 (2023): 84-93. DOI: https://doi.org/10.54216/IJNS.210409

Iampan, A., Rajesh, N., Brundha, B. (2023) 'Neutrosophic set theory applied to Hilbert algebras', International Journal of Neutrosophic Science, Volume 21(Issue 4), pp. 84-93. DOI: https://doi.org/10.54216/IJNS.210409

Iampan A, Rajesh N, Brundha B. Neutrosophic set theory applied to Hilbert algebras. International Journal of Neutrosophic Science. 2023;Volume 21(Issue 4):84-93. DOI: https://doi.org/10.54216/IJNS.210409

A. Iampan, N. Rajesh, B. Brundha, "Neutrosophic set theory applied to Hilbert algebras," International Journal of Neutrosophic Science, vol. Volume 21, no. Issue 4, pp. 84-93, 2023. DOI: https://doi.org/10.54216/IJNS.210409

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