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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 20 , Issue 3 , PP: 45-64, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

The Integration of Rational and Irrational Neutrosophic Functions

Yaser A. Alhasan 1 * , Iqbal A. Musa 2 , Eman A. Abdelgawad 3 , Suliman Sheen 4

  • 1 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia - (y.alhasan@psau.edu.sa)
  • 2 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia - (i.abdulah@psau.edu.sa)
  • 3 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia - (e.abdelwahab@psau.edu.sa)
  • 4 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia - (S.almleh@psau.edu.sa)

    • Doi: https://doi.org/10.54216/IJNS.200305

    Received: October 23, 2022 Accepted: March 04, 2023
    Abstract

    The purpose of this article is to study the integration of rational and irrational neutrosophic functions, where integration of standard rational neutrosophic functions discussed through three cases, in addition, integration of standard irrational neutrosophic functions were introduced through seven cases.

    Keywords :

    neutrosophic proper rational function , neutrosophic integrals , improper rational functions.

    References

    [1]  F.Smarandache,  "Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability ", Sitech-Education Publisher, Craiova – Columbus, 2013. 

    [2]  F.Smarandache  "Finite  Neutrosophic  Complex  Numbers,  by  W.  B.  Vasantha  Kandasamy",  Zip  Publisher, Columbus, Ohio, USA, PP:1-16, 2011.

    [3]  F.Smarandache, "Neutrosophy. / Neutrosophic Probability, Set, and Logic", American Research Press, Rehoboth, USA, 1998.

    [4]  F.Smarandache, "Introduction to Neutrosophic statistics", Sitech-Education Publisher, PP:34-44, 2014.

    [5]  F.Smarandache, "A Unifying Field in Logics: Neutrosophic Logic, Preface by Charles Le, American Research Press,  Rehoboth,  1999,  2000.  Second  edition  of  the  Proceedings  of  the  First  International  Conference  on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics", University of New Mexico, Gallup, 2001. 

    [6]  F.Smarandache,  "Proceedings  of  the  First  International  Conference  on  Neutrosophy",  Neutrosophic  Set, Neutrosophic Probability and Statistics, University of New Mexico, 2001.

    [7]  F.Smarandache, "Neutrosophic Precalculus and Neutrosophic Calculus", book, 2015.

    [8]  Madeleine Al- Tahan, "Some Results on Single Valued Neutrosophic (Weak) Polygroups", International Journal of Neutrosophic Science, Volume 2 , Issue 1, PP: 38-46 , 2020.

    [9]  Y.Alhasan, "The neutrosophic integrals and integration methods", Neutrosophic Sets and Systems, Vo lume 49, pp. 357-374, 2022.

    [10]  A. Chakraborty, "A New Score Function of Pentagonal Neutrosophic Number and its Application in Networking Problem", International Journal of Neutrosophic Science, Volume 1 , Issue 1, PP: 40-51 , 2020

    [11]  A.  Chakraborty,  "Application  of  Pentagonal  Neutrosophic  Number  in  Shortest  Path  Problem",  International =Journal of Neutrosophic Science, Volume 3 , Issue 1, PP: 21-28 , 2020.

    [12]  F.Smarandache,  "Neutrosophy  and  Neutrosophic  Logic,  First  International  Conference  on  Neutrosophy", Neutrosophic Logic, Set, Probability, and Statistics, University of New Mexico, Gallup, NM 87301, USA 2002.

    [13]  Y.Alhasan,  "The  General  Exponential  form  of  a  Neutrosophic  Complex  Number",  International  Journal  of Neutrosophic Science, Volume 11, Issue 2, pp. 100-107, 2020.

    [14]  Abdel-Basset, M., "An approach of TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number", Applied Soft Computing, pp.438-452, 2019.

    [15]   M.Abdel-Baset, V.Chang, A.Gamal, F.Smarandache, "An integrated neutrosophic ANP and VIKOR method for achieving sustainable supplier selection: A case study in importing field", Comput. Ind, pp.94 –110, 2019. 

    [16]  M.Abdel-Basst, R.Mohamed, M.Elhoseny, "<? covid19?> A model for the effective COVID-19 identification inuncertainty environment using primary symptoms and CT scans." Health Informatics Journal, 2020.

    [17]  M.Abdel-Basset, A.Gamal, L.H.Son, F.Smarandache, “A Bipolar Neutrosophic Multi Criteria Decision Making Framework for Professional Selection”. Applied Sciences, 2020.

    [18]  M.Abobala, "On Some Special Substructures of Neutrosophic Rings and Their Properties", International Journal of Neutrosophic Science, Vol 4, pp72-81, 2020.

    [19]  A.Hatip, M. Abobala, "AH-Substructures In Strong Refined Neutrosophic Modules",  International Journal of Neutrosophic Science, Vol. 9, pp. 110-116, 2020.

    [20]  Y.Alhasan, "The neutrosophic integrals and integration methods", Neutrosophic Sets and Systems, Volume 43, pp. 290-301, 2021.

    Cite This Article As :
    A., Yaser. , A., Iqbal. , A., Eman. , Sheen, Suliman. The Integration of Rational and Irrational Neutrosophic Functions. International Journal of Neutrosophic Science, vol. , no. , 2023, pp. 45-64. DOI: https://doi.org/10.54216/IJNS.200305
    A., Y. A., I. A., E. Sheen, S. (2023). The Integration of Rational and Irrational Neutrosophic Functions. International Journal of Neutrosophic Science, (), 45-64. DOI: https://doi.org/10.54216/IJNS.200305
    A., Yaser. A., Iqbal. A., Eman. Sheen, Suliman. The Integration of Rational and Irrational Neutrosophic Functions. International Journal of Neutrosophic Science , no. (2023): 45-64. DOI: https://doi.org/10.54216/IJNS.200305
    A., Y. , A., I. , A., E. , Sheen, S. (2023) . The Integration of Rational and Irrational Neutrosophic Functions. International Journal of Neutrosophic Science , () , 45-64 . DOI: https://doi.org/10.54216/IJNS.200305
    A. Y. , A. I. , A. E. , Sheen S. [2023]. The Integration of Rational and Irrational Neutrosophic Functions. International Journal of Neutrosophic Science. (): 45-64. DOI: https://doi.org/10.54216/IJNS.200305
    A., Y. A., I. A., E. Sheen, S. "The Integration of Rational and Irrational Neutrosophic Functions," International Journal of Neutrosophic Science, vol. , no. , pp. 45-64, 2023. DOI: https://doi.org/10.54216/IJNS.200305

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