2142 1397
Full Length Article
International Journal of Neutrosophic Science
Volume 3 , Issue 2, PP: 89-107 , 2020 | Cite this article as | XML | Html |PDF

Title

Image and Inverse Image of Neutrosophic Cubic Sets in UP-Algebras under UP-Homomorphisms

  Metawee Songsaeng 1 * ,   Aiyared Iampan 2

1  Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand
    (metawee.faith@gmail.com)

2  Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand
    (aiyared.ia@up.ac.th)


Doi   :   https://doi.org/10.54216/IJNS.030201


Abstract :

The concept of a neutrosophic cubic set in a UP-algebra was introduced by Songsaeng and Iampan [Neu-trosophic cubic set theory applied to UP-algebras, 2019]. In this paper, we define the image and inverse image of a neutrosophic cubic set in a non-empty set under any function and study the image and inverse image of a neutrosophic cubic UP-subalgebra (resp., neutrosophic cubic near UP-filter, neutrosophic cubic UP-filter, neutrosophic cubic UP-ideal, neutrosophic cubic strong UP-ideal) of a UP-algebra under some UP-homomorphisms.

Keywords :

UP-algebra , UP-homomorphism , neutrosophic cubic UP-subalgebra , neutrosophic cubic near UP-filter , neutrosophic cubic UP-filter , neutrosophic cubic UP-ideal , neutrosophic cubic strong UP-ideal

References :

[1] Al-Tahan, M.; Davvaz, B. Neutrosophic ℵ-ideals (ℵ-subalgebras) of subtraction algebra. Int. J. Neutro-sophic Sci. 2020, 3(1), 44–53.

[2] Ansari, M. A.; Haidar, A.; Koam, A. N. A. On a graph associated to UP-algebras. Math. Comput. Appl. 2018, 23(4), 61.

[3] Ansari, M. A.; Koam, A. N. A.; Haider, A. Rough set theory applied to UP-algebras. Ital. J. Pure Appl. Math. 2019, 42, 388–402.

[4] Dokkhamdang, N.; Kesorn, A.; Iampan, A. Generalized fuzzy sets in UP-algebras. Ann. Fuzzy Math. Inform. 2018, 16(2), 171–190.

[5] Guntasow, T.; Sajak, S.; Jomkham, A.; Iampan, A. Fuzzy translations of a fuzzy set in UP-algebras. J. Indones. Math. Soc. 2017, 23(2), 1–19.

[6] Iampan, A. Multipliers and near UP-filters of UP-algebras. J. Discrete Math. Sci. Cryptography (in press).

[7] Iampan, A. A new branch of the logical algebra: UP-algebras. J. Algebra Relat. Top. 2017, 5(1), 35–54.

[8] Iampan, A. Introducing fully UP-semigroups. Discuss. Math., Gen. Algebra Appl. 2018, 38(2), 297–306.

[9] Iampan, A. The UP-isomorphism theorems for UP-algebras. Discuss. Math., Gen. Algebra Appl. 2019, 39(1), 113–123.

[10] Ibrahim, M. A.; Agboola, A. A. A.; Adeleke, E. O.; Akinleye, S. A. Introduction to neutrosophic subtraction algebra and neutrosophic subtraction semigroup. Int. J. Neutrosophic Sci. 2020, 2(1), 47–62.

[11] Iqbal, R.; Zafar, S.; Sardar, M. S. Neutrosophic cubic subalgebras and neutrosophic cubic closed ideals of B-algebras. Neutrosophic Sets Syst. 2016, 14, 47–60.

[12] Jun, Y. B.; Kim, C. S.; Yang, K. O. Cubic sets. Ann. Fuzzy Math. Inform. 2012, 4(1), 83–98.

[13] Jun, Y. B.; Kim, S. J.; Smarandache, F. Interval neutrosophic sets with applications in BCK/BCI-algebra. Axioms 2018, 7(2), 23–35.

[14] Jun, Y. B.; Smarandache, F.; Bordbar, H. Neutrosophic N -structures applied to BCK/BCI-algebras. Inform. 2017, 8(4), 128.

[15] Jun, Y. B.; Smarandache, F.; Kim, C. S. Neutrosophic cubic sets. New Math. Nat. Comput. 2017, 13(1), 41–54.

[16] Kaijae, W.; Poungsumpao, P.; Arayarangsi, S.; Iampan, A. UP-algebras characterized by their anti-fuzzy UP-ideals and anti-fuzzy UP-subalgebras. Ital. J. Pure Appl. Math. 2016, 36, 667–692.

[17] Kesorn, B.; Maimun, K.; Ratbandan, W.; Iampan, A. Intuitionistic fuzzy sets in UP-algebras. Ital. J. Pure Appl. Math. 2015, 34, 339–364.

[18] Khalid, M.; Khalid, N. A.; Khalid, H.; Broumi, S. Multiplicative interpretation of neutrosophic cubic set on B-algebra. Int. J. Neutrosophic Sci. 2020, 1(2), 64–73.

[19] Khan, M.; Anis, S.; Smarandache, F.; Jun, Y. B. Neutrosophic N -structures and their applications in semigroups. Ann. Fuzzy Math. Inform. 2017, 14(6), 583–598.

[20] Mordeson, J. N.; Malik, D. S.; Kuroki, N. Fuzzy Semigroups, volume 131; Springer, 2012.

[21] Prabpayak, C.; Leerawat, U. On ideals and congruences in KU-algebras. Sci. Magna 2009, 5(1), 54–57.

[22] Satirad, A.; Mosrijai, P.; Iampan, A. Formulas for finding UP-algebras. Int. J. Math. Comput. Sci. 2019, 14(2), 403–409.

[23] Satirad, A.; Mosrijai, P.; Iampan, A. Generalized power UP-algebras. Int. J. Math. Comput. Sci. 2019, 14(1), 17–25.

[24] Senapati, T.; Jun, Y. B.; Shum, K. P. Cubic set structure applied in UP-algebras. Discrete Math. Algo-rithms Appl. 2018, 10(4), 1850049.

[25] Senapati, T.; Muhiuddin, G.; Shum, K. P. Representation of UP-algebras in interval-valued intuitionistic fuzzy environment. Ital. J. Pure Appl. Math. 2017, 38, 497–517.

[26] Smarandache, F. A Unifying Field in Logic: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neu-trosophic Probability; American Research Press, Rehoboth, NM, 1999.

[27] Somjanta, J.; Thuekaew, N.; Kumpeangkeaw, P.; Iampan, A. Fuzzy sets in UP-algebras. Ann. Fuzzy Math. Inform. 2016, 12(6), 739–756.

[28] Songsaeng, M.; Iampan, A. N -fuzzy UP-algebras and its level subsets. J. Algebra Relat. Top. 2018, 6(1), 1–24.

[29] Songsaeng, M.; Iampan, A. Fuzzy proper UP-filters of UP-algebras. Honam Math. J. 2019, 41(3), 515–530.

[30] Songsaeng, M.; Iampan, A. Neutrosophic cubic set theory applied to UP-algebras. Thai J. Math. (ac-cepted).

[31] Songsaeng, M.; Iampan, A. Neutrosophic set theory applied to UP-algebras. Eur. J. Pure Appl. Math. 2019, 12(4), 1382–1409.

[32] Songsaeng, M.; Iampan, A. Neutrosophic sets in UP-algebras by means of interval-valued fuzzy sets. J. Int. Math. Virtual Inst. 2020, 10(1), 93–122.

[33] Songsaeng, M.; Iampan, A. A novel approach to neutrosophic sets in UP-algebras. J. Math. Computer Sci. 2020, 21(1), 78–98.

[34] Sripaeng, S.; Tanamoon, K.; Iampan, A. On anti Q-fuzzy UP-ideals and anti Q-fuzzy UP-subalgebras of UP-algebras. J. Inf. Optim. Sci. 2018, 39(5), 1095–1127.

[35] Taboon, K.; Butsri, P.; Iampan, A. A cubic set theory approach to UP-algebras. J. Interdiscip. Math.(accepted).

[36] Tanamoon, K.; Sripaeng, S.; Iampan, A. Q-fuzzy sets in UP-algebras. Songklanakarin J. Sci. Technol. 2018, 40(1), 9–29.

[37] Wang, H.; Smarandache, F.; Zhang, Y. Q.; Sunderraman, R. Interval Neutrosophic Sets and logic: Theory and Applications in Computing; Hexis, Phoenix, Ariz, USA, 2005.

[38] Zadeh, L. A. Fuzzy sets. Inf. Cont. 1965, 8, 338–353.

[39] Zadeh, L. A. The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 1975, 8, 199–249.


Cite this Article as :
Style #
MLA Metawee Songsaeng, Aiyared Iampan. "Image and Inverse Image of Neutrosophic Cubic Sets in UP-Algebras under UP-Homomorphisms." International Journal of Neutrosophic Science, Vol. 3, No. 2, 2020 ,PP. 89-107 (Doi   :  https://doi.org/10.54216/IJNS.030201)
APA Metawee Songsaeng, Aiyared Iampan. (2020). Image and Inverse Image of Neutrosophic Cubic Sets in UP-Algebras under UP-Homomorphisms. Journal of International Journal of Neutrosophic Science, 3 ( 2 ), 89-107 (Doi   :  https://doi.org/10.54216/IJNS.030201)
Chicago Metawee Songsaeng, Aiyared Iampan. "Image and Inverse Image of Neutrosophic Cubic Sets in UP-Algebras under UP-Homomorphisms." Journal of International Journal of Neutrosophic Science, 3 no. 2 (2020): 89-107 (Doi   :  https://doi.org/10.54216/IJNS.030201)
Harvard Metawee Songsaeng, Aiyared Iampan. (2020). Image and Inverse Image of Neutrosophic Cubic Sets in UP-Algebras under UP-Homomorphisms. Journal of International Journal of Neutrosophic Science, 3 ( 2 ), 89-107 (Doi   :  https://doi.org/10.54216/IJNS.030201)
Vancouver Metawee Songsaeng, Aiyared Iampan. Image and Inverse Image of Neutrosophic Cubic Sets in UP-Algebras under UP-Homomorphisms. Journal of International Journal of Neutrosophic Science, (2020); 3 ( 2 ): 89-107 (Doi   :  https://doi.org/10.54216/IJNS.030201)
IEEE Metawee Songsaeng, Aiyared Iampan, Image and Inverse Image of Neutrosophic Cubic Sets in UP-Algebras under UP-Homomorphisms, Journal of International Journal of Neutrosophic Science, Vol. 3 , No. 2 , (2020) : 89-107 (Doi   :  https://doi.org/10.54216/IJNS.030201)