International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 22 , Issue 1 , PP: 60-76, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups

Ashraf Al-Quran 1 * , Faisal Al-Sharqi 2 , Zahari Md. Rodzi 3 , Mona Aladil 4 , Rawan A. shlaka 5 , Mamika Ujianita Romdhini 6 , Mohammad K. Tahat 7 , Obadah Said Solaiman 8

  • 1 Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia - (aalquran@kfu.edu.sa)
  • 2 Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq - (faisal.ghazi@uoanbar.edu.iq)
  • 3 College of Computing, Informatics and Mathematics, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 70300 Negeri Sembilan, Malaysia - (zahari@uitm.edu.my)
  • 4 Curricula and Teaching Methods Department, College of Education, King Faisal University, Al-Ahsa 31982, Saudi Arabia - (maladail@kfu.edu.sa)
  • 5 College of Pharmacy, National University of Science and Technology, Dhi Qar, Iraq - (rawan-a.shlaka@nust.edu.iq;)
  • 6 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Mataram, Mataram, 83125,Indonesia - (mamika@unram.ac.id)
  • 7 Academic Department, Saudi Petroleum Services Polytechnic,Dammam, Saudi Arabia - (tahatmo@spsp.edu.sa)
  • 8 Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia,Bangi 43600, Selangor, Malaysia - (obadah sy@yahoo.com)
  • Doi: https://doi.org/10.54216/IJNS.220105

    Received: March 23, 2023 Revised: June 25, 2023 Accepted: September 01, 2023
    Abstract

    Groups and subgroups are rich algebraic structures, and both of them depend on binary operations in their work. The discussion of this paper is organized into two parts. In the first part, we define the notion of Qcomplex neutrosophic soft sets (Q-CNSSs) by amalgamating two previous models of Q-complex neutrosophic set (Q-CNS) and soft set (SS) to address the issues of two-dimensionality (two variables) in a universal set under a parametric environment. Subsequently, the relation between Q-CNSSs and Q- neutrosophic soft sets (Q-NSSs) is verified. A basic set theory for this hybrid model is developed. In particular, null Q-CNSS and absolute Q-CNSS are defined. The basic operators of the complement, subset, equality, union and intersection are advanced and their properties are examined. Further, the notions of the homogeneous and completely homogeneous Q-CNSSs are proposed along with some illustrated examples. In part two, we move to study some algebraic structures of this model when we define the notions of Q-complex neutrosophic soft groups (QCNSG) and Q-complex neutrosophic soft subgroups (Q-CNSSG). Then, the relation between Q-CNSG and Q-neutrosophic soft group (Q-NSG) is scrutinized. Moreover, the algebraic properties of the Q-CNSG and Q-CNSSG are discussed and verified. Finally, some theories that show the relationship between the Q-CNSG and the soft group are proposed.

    Keywords :

    Complex neutrosophic set: Soft set , Soft group , Q-neutrosophic set , Q- complex neutrosophic set

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    Cite This Article As :
    Al-Quran, Ashraf. , Al-Sharqi, Faisal. , Md., Zahari. , Aladil, Mona. , A., Rawan. , Ujianita, Mamika. , K., Mohammad. , Said, Obadah. The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups. Journal of International Journal of Neutrosophic Science, vol. 22, no. 1, 2023, pp. 60-76. DOI: https://doi.org/10.54216/IJNS.220105
    Al-Quran, A. Al-Sharqi, F. Md., Z. Aladil, M. A., R. Ujianita, M. K., M. Said, O. (2023). The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups. Journal of International Journal of Neutrosophic Science, 22( 1), 60-76. DOI: https://doi.org/10.54216/IJNS.220105
    Al-Quran, Ashraf. Al-Sharqi, Faisal. Md., Zahari. Aladil, Mona. A., Rawan. Ujianita, Mamika. K., Mohammad. Said, Obadah. The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups. Journal of International Journal of Neutrosophic Science 22, no. 1 (2023): 60-76. DOI: https://doi.org/10.54216/IJNS.220105
    Al-Quran, A. , Al-Sharqi, F. , Md., Z. , Aladil, M. , A., R. , Ujianita, M. , K., M. , Said, O. (2023) . The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups. Journal of International Journal of Neutrosophic Science , 22( 1) , 60-76 . DOI: https://doi.org/10.54216/IJNS.220105
    Al-Quran A. , Al-Sharqi F. , Md. Z. , Aladil M. , A. R. , Ujianita M. , K. M. , Said O. [2023]. The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups. Journal of International Journal of Neutrosophic Science. 22( 1): 60-76. DOI: https://doi.org/10.54216/IJNS.220105
    Al-Quran, A. Al-Sharqi, F. Md., Z. Aladil, M. A., R. Ujianita, M. K., M. Said, O. "The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups," Journal of International Journal of Neutrosophic Science, vol. 22, no. 1, pp. 60-76, 2023. DOI: https://doi.org/10.54216/IJNS.220105