Journal of Neutrosophic and Fuzzy Systems

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Journal of Neutrosophic and Fuzzy Systems

Volume 4 , Issue 1 , PP: 41-8, 2022 | Cite this article as | XML | Html | PDF

Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers

Ahmad Salama 1 * , Rasha Dalla 2 , Malath Al Aswad 3 , Rozina Ali 4

  • 1 Department of Mathematics, port said, Egypt - (drsalama44@gmail.com)
  • 2 Departement of Mathematics, Albaath University, Homs, Syria - ( rasha.dallah20@gmail.com)
  • 3 PHD of Mathematics, GaziAntep, Turkey - (Malaz.Aswad@yahoo.com)
  • 4 Department Of Mathematics, Cairo University, Egypt - (rozyyy123n@gmail.com)
  • Doi: https://doi.org/10.54216/JNFS.040105

    Received: April 16, 2022 Accepted: August 18, 2022
    Abstract

    This paper is dedicated to define for the first time the concept of 2-cyclic complex refined neutrosophic numbers as a direct application of 2-cyclic refined neutrosophic sets. Also, it presents some of their elementary properties such as conjugates, absolute values, invertibility, and algebraic operations.

    Also, we illustrate many examples to clarify the validity of our discussion

    Keywords :

    refined neutrosophic complex number , cyclic refined neutrosophic complex number , refined neutrosophic real number, invertible number.

    References

    [1] Abobala, M., "AH-Subspaces in Neutrosophic Vector Spaces", International Journal of Neutrosophic

    Science, Vol. 6 , pp. 80-86. 2020.

    [2] Abobala, M.,. "A Study of AH-Substructures in n-Refined Neutrosophic Vector Spaces", International

    Journal of Neutrosophic Science", Vol. 9, pp.74-85. 2020.

    [3] Sankari, H., and Abobala, M., "Neutrosophic Linear Diophantine Equations With two Variables",

    Neutrosophic Sets and Systems, Vol. 38, pp. 22-30, 2020.

    [4] Sankari, H., and Abobala, M." n-Refined Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 36,

    pp. 1-11. 2020.

    [5] Alhamido, R., and Abobala, M., "AH-Substructures in Neutrosophic Modules", International Journal of

    Neutrosophic Science, Vol. 7, pp. 79-86 . 2020.

    [6]Smarandache, F., " A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set,

    Neutrosophic Probability", American Research Press. Rehoboth, 2003.

    [7]Suresh, R., and S. Palaniammal,. "Neutrosophic Weakly Generalized open and Closed Sets", Neutrosophic

    Sets and Systems, Vol. 33, pp. 67-77,. 2020.

    [8]Olgun, N., and Hatip, A., "The Effect Of The Neutrosophic Logic On The Decision Making, in Quadruple

    Neutrosophic Theory And Applications", Belgium, EU, Pons Editions Brussels,pp. 238-253. 2020.

    [9]Hatip, A., Alhamido, R., and Abobala, M., "A Contribution to Neutrosophic Groups", International Journal

    of Neutrosophic Science", Vol. 0, pp. 67-76 . 2019.

    [10] Abobala, M., " n-Refined Neutrosophic Groups I", International Journal of Neutrosophic Science, Vol. 0,

    pp. 27-34. 2020.

    [11]Abobala, M., "Classical Homomorphisms Between n-refined Neutrosophic Rings", International Journal of

    Neutrosophic Science", Vol. 7, pp. 74-78. 2020.

    [12]Smarandache, F., and Abobala, M., n-Refined neutrosophic Rings, International Journal of Neutrosophic

    Science, Vol. 5 , pp. 83-90, 2020.

    [13]Abobala, M., On Some Special Substructures of Neutrosophic Rings and Their Properties, International

    Journal of Neutrosophic Science", Vol. 4 , pp. 72-81, 2020.

    [14] Abobala, M., "On Some Special Substructures of Refined Neutrosophic Rings", International Journal of

    Neutrosophic Science, Vol. 5, pp. 59-66. 2020.

    [15]Sankari, H., and Abobala, M.," AH-Homomorphisms In neutrosophic Rings and Refined Neutrosophic

    Rings", Neutrosophic Sets and Systems, Vol. 38, pp. 101-112, 2020.

    [16]Smarandache, F., and Kandasamy, V.W.B., " Finite Neutrosophic Complex Numbers",·Source: arXiv. 2011.

    [17] Agboola, A.A.A,. Akwu, A.D,. and Oyebo, Y.T., " Neutrosophic Groups and Subgroups", International .J

    .Math. Combin, Vol. 3, pp. 1-9. 2012.

    [18]Smarandache, F., " n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in

    Physics, 143-146, Vol. 4, 2013.

    [19]Adeleke, E.O., Agboola, A.A.A.,and Smarandache, F., "Refined Neutrosophic Rings I", International

    Journal of Neutrosophic Science, Vol. 2(2), pp. 77-81. 2020.

    [20]Hatip, A., and Abobala, M., "AH-Substructures In Strong Refined Neutrosophic Modules", International

    Journal of Neutrosophic Science, Vol. 9, pp. 110-116 . 2020.

    [21]Smarandache F., and Abobala, M., "n-Refined Neutrosophic Vector Spaces", International Journal of

    Neutrosophic Science, Vol. 7, pp. 47-54. 2020.

    [22]Sankari, H., and Abobala, M., "Solving Three Conjectures About Neutrosophic Quadruple Vector Spaces",

    Neutrosophic Sets and Systems, Vol. 38, pp. 70-77. 2020.

    [23]Adeleke, E.O., Agboola, A.A.A., and Smarandache, F., "Refined Neutrosophic Rings II", International

    Journal of Neutrosophic Science, Vol. 2(2), pp. 89-94. 2020.

    [24]Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic

    Equations, Journal Of Mathematics, Hindawi, 2021

    [25]Abobala, M., A Study of Maximal and Minimal Ideals of n-Refined Neutrosophic Rings, Journal of Fuzzy

    Extension and Applications, Vol. 2, pp. 16-22, 2021.

    [26]Abobala, M., " Semi Homomorphisms and Algebraic Relations Between Strong Refined Neutrosophic

    Modules and Strong Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 39, 2021.

    [27]Giorgio, N, Mehmood, A., and Broumi, S.," Single Valued neutrosophic Filter", International Journal of

    Neutrosophic Science, Vol. 6, 2020.

    [28]Chellamani, P., and Ajay, D., "Pythagorean neutrosophic Fuzzy Graphs", International Journal of

    Neutrosophic Science, Vol. 11, 2021.

    [29]Milles, S, Barakat, M, and Latrech, A., " Completeness and Compactness In Standard Single Valued

    neutrosophic Metric Spaces", International Journal of Neutrosophic Science, Vol.12 , 2021.

    [30]Abobala, M., "On Some Neutrosophic Algebraic Equations", Journal of New Theory, Vol. 33, 2020.

    [31]Abobala, M., On The Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations,

    Journal of Mathematics, Hindawi, 2021.

    [32] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined

    Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021

    [33] Kandasamy V, Smarandache F., and Kandasamy I., Special Fuzzy Matrices for Social Scientists . Printed in

    the United States of America,2007, book, 99 pages.

    [34] Khaled, H., and Younus, A., and Mohammad, A., " The Rectangle Neutrosophic Fuzzy Matrices", Faculty

    of Education Journal Vol. 15, 2019. (Arabic version).

    [35]Abobala, M., Partial Foundation of Neutrosophic Number Theory, Neutrosophic Sets and Systems, Vol. 39 ,

    2021.

    [36] F. Smarandache, Neutrosophic Theory and Applications, Le Quy Don Technical University, Faculty of

    Information technology, Hanoi, Vietnam, 17th May 2016.

    [37]Ibrahim, M.A., Agboola, A.A.A, Badmus, B.S. and Akinleye, S.A., "On refined Neutrosophic Vector Spaces

    I", International Journal of Neutrosophic Science, Vol. 7, pp. 97-109. 2020.

    [38]Ibrahim, M.A., Agboola, A.A.A, Badmus, B.S., and Akinleye, S.A., "On refined Neutrosophic Vector

    Spaces II", International Journal of Neutrosophic Science, Vol. 9, pp. 22-36. 2020.

    [39]Abobala, M, "n-Cyclic Refined Neutrosophic Algebraic Systems Of Sub-Indeterminacies, An Application

    To Rings and Modules", International Journal of Neutrosophic Science, Vol. 12, pp. 81-95 . 2020.

    [40]Smarandache, F., "Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets", Inter. J. Pure Appl.

    Math., pp. 287-297. 2005.

    [41] Abobala, M., "On Some Special Elements In Neutrosophic Rings and Refined Neutrosophic Rings", Journal

    of New Theory, vol. 33, 2020.

    [42]Abobala, M., Hatip, A., Olgun, N., Broumi, S., Salama, A,A., and Khaled, E, H., The algebraic creativity In

    The Neutrosophic Square Matrices, Neutrosophic Sets and Systems, Vol. 40, pp. 1-11, 2021.

    [43]Smarandache, F., and Kandasamy, V.W.B., " Finite Neutrosophic Complex Numbers",·Source: arXiv. 2011.

    [44]Aswad, F, M., " A Study of A Neutrosophic Complex Numbers and Applications", Neutrosophic

    Knowledge, Vol. 1, 2020.

    [45] Abobala, M., Hatip, A., Bal,M.," A Study Of Some Neutrosophic Clean Rings", International journal of

    neutrosophic science, 2022.

    [46] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings",

    Neutrosophic Sets and Systems, Vol. 45, 2021.

    [47] Olgun, N., Hatip, A., Bal, M., and Abobala, M., " A Novel Approach To Necessary and Sufficient

    Conditions For The Diagonalization of Refined Neutrosophic Matrices", International Journal of neutrosophic

    Science, Vol. 16, pp. 72-79, 2021.

    [48] Abobala, M., Hatip, A., and Bal, M., " A Review On Recent Advantages In Algebraic Theory Of

    Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol.17, 2021.

    [49] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", Neutrosophic

    sets and systems, Vol. 45, 2021.

    [50] Abobala, M., Bal, M., Aswad, M., "A Short Note On Some Novel Applications of Semi Module

    Homomorphisms", International journal of neutrosophic science, 2022.

    [51] Singh, P,K., " Data With Turiyam Set for Fourth Dimension Quantum Information Processing", Journal of

    Neutrosophic and Fuzzy Systems, vol.1, 2022.

    [52] Singh, P, K., Ahmad, K., Bal, M., Aswad, M.," On The Symbolic Turiyam Rings", Journal of Neutrosophic

    and Fuzzy Systems, 2022.

    [53] Prem Kumar Singh, Three-way n-valued neutrosophic concept lattice at different granulation, International

    Journal of Machine Learning and Cybernetics, Springer, November 2018, Vol 9, Issue 11, pp. 1839-1855.

    Cite This Article As :
    Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. "Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers." Full Length Article, Vol. 4, No. 1, 2022 ,PP. 41-8 (Doi   :  https://doi.org/10.54216/JNFS.040105)
    Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. (2022). Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers. Journal of , 4 ( 1 ), 41-8 (Doi   :  https://doi.org/10.54216/JNFS.040105)
    Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. "Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers." Journal of , 4 no. 1 (2022): 41-8 (Doi   :  https://doi.org/10.54216/JNFS.040105)
    Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. (2022). Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers. Journal of , 4 ( 1 ), 41-8 (Doi   :  https://doi.org/10.54216/JNFS.040105)
    Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers. Journal of , (2022); 4 ( 1 ): 41-8 (Doi   :  https://doi.org/10.54216/JNFS.040105)
    Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali, Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers, Journal of , Vol. 4 , No. 1 , (2022) : 41-8 (Doi   :  https://doi.org/10.54216/JNFS.040105)