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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 26 , Issue 1 , PP: 283-292, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Neutrosophic subgroups and neutrosophic normal subgroups of groups

Aiyared Iampan 1 * , C. Sivakumar 2 , Neelamegarajan Rajesh 3

  • 1 Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Mae Ka, Mueang, Phayao 56000, Thailand - (aiyared.ia@up.ac.th)
  • 2 Department of Mathematics, Thanthai Periyar Government Arts and Science College (affiliated to Bharathidasan University), Tiruchirappalli 624024, Tamil Nadu, India - (sivaias777@gmail.com)
  • 3 Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathidasan University), Thanjavur-613005, Tamil Nadu, India - (nrajesh topology@yahoo.co.in)

    • Doi: https://doi.org/10.54216/IJNS.260124

    Received: October 27, 2024 Revised: January 06, 2025 Accepted: February 17, 2025
    Abstract

    In this paper, we introduce the concepts of neutrosophic subgroups and neutrosophic normal subgroups of groups and investigate several properties. We investigate relations between neutrosophic subgroups (neutrosophic normal subgroups) and their neutrosophic level subsets of a group. We also look at the homomorphic image and inverse image of the neutrosophic subgroups and neutrosophic normal subgroups of groups, as well as some related properties.

    Keywords :

    Group , Neutrosophic set , Neutrosophic subgroup , Neutrosophic normal subgroup

    References

    [1] N. Ajmal and A. S. Prajapati, Fuzzy cosets and fuzzy normal subgroups, Inf. Sci., 64(1), (1992), 17-25. https://doi.org/10.1016/0020-0255(92)90107-J

    [2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1), (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3

    [3] S. Bhunia, G. Ghorai and Q. Xin, On the characterization of neutrosophic subgroups, AIMS Math., 6(1), (2021), 962-978. https://doi.org/10.3934/math.2021058

    [4] S. Bhunia and G. Ghorai, An approach to Lagrange’s theorem in Pythagorean fuzzy subgroups, Kragujevac J. Math., 48(6), (2024), 893-906.

    [5] J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, Fuzzy group theory, Springer-Verlag, New York, 2005.

    [6] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35(3), (1971), 512-517. https://doi.org/10.1016/0022-247X(71)90199-5

    [7] R. L. Roth, A history of Lagrange’s theorem on groups, Math. Mag., 74(2), (2001), 99-108. https: //doi.org/10.1080/0025570X.2001.11953045

    [8] F. Smarandache, A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability and statistics (fourth edition), American Research Press, Rehoboth, 2005.

    [9] F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24(3), (2005), 287-297.

    [10] V. Cetkin and H. Aygun, An approach to neutrosophic subgroup and its fundamental properties, J. Intell. Fuzzy Syst., 29, (2015), 1941-1947. https://doi.org/10.3233/IFS-151672

    [11] R. R. Yager, Pythagorean fuzzy subsets, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, AB, Canada, 2013, 57-61. https://doi.org/10.1109/ IFSA-NAFIPS.2013.6608375

    [12] L. A. Zadeh, Fuzzy sets, Inf. Control, 8(3), (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X

     

    Cite This Article As :
    Iampan, Aiyared. , Sivakumar, C.. , Rajesh, Neelamegarajan. Neutrosophic subgroups and neutrosophic normal subgroups of groups. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 283-292. DOI: https://doi.org/10.54216/IJNS.260124
    Iampan, A. Sivakumar, C. Rajesh, N. (2025). Neutrosophic subgroups and neutrosophic normal subgroups of groups. International Journal of Neutrosophic Science, (), 283-292. DOI: https://doi.org/10.54216/IJNS.260124
    Iampan, Aiyared. Sivakumar, C.. Rajesh, Neelamegarajan. Neutrosophic subgroups and neutrosophic normal subgroups of groups. International Journal of Neutrosophic Science , no. (2025): 283-292. DOI: https://doi.org/10.54216/IJNS.260124
    Iampan, A. , Sivakumar, C. , Rajesh, N. (2025) . Neutrosophic subgroups and neutrosophic normal subgroups of groups. International Journal of Neutrosophic Science , () , 283-292 . DOI: https://doi.org/10.54216/IJNS.260124
    Iampan A. , Sivakumar C. , Rajesh N. [2025]. Neutrosophic subgroups and neutrosophic normal subgroups of groups. International Journal of Neutrosophic Science. (): 283-292. DOI: https://doi.org/10.54216/IJNS.260124
    Iampan, A. Sivakumar, C. Rajesh, N. "Neutrosophic subgroups and neutrosophic normal subgroups of groups," International Journal of Neutrosophic Science, vol. , no. , pp. 283-292, 2025. DOI: https://doi.org/10.54216/IJNS.260124

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