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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 17 , Issue 2 , PP: 87-95, 2021 | Cite this article as | XML | Html | PDF | Full Length Article

n-Valued Refined Neutrosophic Crisp Sets

Ahmed B. AL-Nafee 1 * , Said Broumi 2 , Luay A. Al-Swidi 3

  • 1 Ministry of Education Open Educational College, Department of Mathematics, Babylon, Iraq - (Ahm_math_88@yahoo.com)
  • 2 Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, B.P 7955, Morocco. - ( broumisaid78@gmail.com)
  • 3 Department of Mathematics, University of Babylon, Iraq, pure.leal.abd@uobabylon.edu.iq - (pure.leal.abd@uobabylon.edu.iq)

    • Doi: https://doi.org/10.54216/IJNS.170201

    Received: September 10, 2021 Accepted: December 03, 2021
    Abstract

    The main purpose of this manuscript is to expand the notion of neutrosophic crisp set (NCS) by presenting the notion of n-valued refined neutrosophic crisp set with some illustration examples. We also establish some of its set-theoretical operations.

    Keywords :

    Neutrosophic Crisp Set, n-Valued Refined Neutrosophic Crisp Set,  , Quadripartitioned  , Neutrosophic Crisp Set,  , Pentapartitioned  , Neutrosophic Crisp Set.

    References

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    [2]    F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math. 24 (2005) 287–297.

    [3]   A.A.Salama and F.Smarandache, Neutrosophic crisp set theory, Neutrosophic Sets and Systems 2014, 5, 27–35.

    [4]   A.A.Salama, F.Smarandache, Neutrosophic Crisp Set Theory; Educational Publisher: Columbus, 2015. 

    [5]   Coker, D. (1996). A note on intuitionistic sets and intuitionistic points. Turkish Journal of Mathematics, 20(3), 343-351.

    [6]   Salama, A. A., Florentin Smarandache, and Valeri Kroumov. "Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces." Neutrosophic Sets and Systems 2.1 (2014).

    [7]   Kharal, A., A Neutrosophic Multicriteria Decision Making Method, New Mathematics and Natural Computation, Creighton University, USA,2013. 

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    [10] AL-Nafee, A. B., Al-Hamido, R. K., & Smarandache, F. (2019). Separation Axioms in Neutrosophic Crisp Topological Spaces. Neutrosophic Sets & Systems, 25.‏ pp. 25 – 33.

    [11] AL-Nafee, A. B., Smarandache, F., & Salama, A. A. (2020). New Types of Neutrosophic Crisp Closed Sets. Neutrosophic Sets & Systems, 36.‏ pp. 175 -183.

    [12] AL-Nafee, A. B. (2020). New Family of Neutrosophic Soft Sets. Neutrosophic Sets & Systems, (38).‏ pp. 482 – 496.

    [13] Ahmed B. AL-Nafee, Said Broumi, & Florentin Smarandache. (2021). Neutrosophic Soft Bitopological Spaces. International Journal of Neutrosophic Science, 14(1), 47–56. http://doi.org/10.5281/zenodo.4725946.

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    [15] Salama, A. A., Alblowi, S. A., Smarandache, F.“Neutrosophic crisp open set and neutrosophic crisp continuity via neutrosophic crisp ideals”. I.J. Information Engineering and Electronic Business vol. 3, pp.1 – 8, 2014. 

    [16] A. Salama.“Basic Structure of Some Classes of Neutrosophic Crisp Nearly Open Sets and Possible Application to GIS Topology”. Neutrosophic Sets and Systems, vol.(7),18-22. 2015.

    [17] I. M. Hanafy, A. Salama and K.M. Mahfouz. “Neutrosophic Crisp Events and Its Probability”. International Journal of Mathematics and Computer Applications Research (IJMCAR), vol. 3, no1, pp.171-178,2013.

    [18] Salama, A. A., Smarandache, F, “Filters via Neutrosophic Crisp Sets”, Neutrosophic Sets and Systems, Vol. 1, No. 1, pp. 34-38, 2013. 

    [19] A.A. Salama, Mohamed Fazaa, Mohamed Yahya, M. Kazim, A Suggested Diagnostic System of Corona Virus based on the Neutrosophic Systems and Deep Learning, I. J. Neutrosophic Science, Vol.9(1), 2020,pp54-59.

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    [21] Zhang, Xiaohong, Mengyuan Li, and Tao Lei. "On Neutrosophic Crisp Sets and Neutrosophic Crisp Mathematical Morphology." Neutrosophic Sets and Systems 43 (2021): 1-11.

    [22] Chatterjee, R., Majumdar, P., & Samanta, S. K. (2016). On some similarity measures and entropy on quadripartitioned single valued neutrosophic sets. Journal of Intelligent & Fuzzy Systems, 30(4), 2475-2485.

    [23] Belnap, N. D. (1977). A useful four-valued logic. In Modern uses of multiple-valued logic (pp. 5-37). Springer, Dordrecht. ‏

    [24] F. Smarandache, ’n’-valued refined neutrosophic logic and its applications in physics, Progress in Physics, 4:143–146, 2013.

    [25] Alkhazaleh, S. (2017). n-Valued refined neutrosophic soft set theory. Journal of Intelligent & Fuzzy Systems, 32(6), 4311-4318.

    [26] Alkhazaleh, S., & Hazaymeh, A. A. (2017). N-valued refined neutrosophic soft sets and their applications in decision making problems and medical diagnosis. Infinite Study. ‏

    [27] Mallick, R., & Pramanik, S. (2020). Pentapartitioned neutrosophic set and its properties. Neutrosophic Sets and Systems, 36, 184-192. ‏

    [28] Ahmed B. AL-Nafee , Jamal K. Obeed , Huda E. Khalid, Continuity and Compactness on Neutrosophic Soft Bitopological Spaces, International Journal of Neutrosophic Science, Vol. 16 , No. 2 , pp. 62-71 , 2021 (Doi   :  https://doi.org/10.54216/IJNS.160201)

     

    ‏

    Cite This Article As :
    B., Ahmed. , Broumi, Said. , A., Luay. n-Valued Refined Neutrosophic Crisp Sets. International Journal of Neutrosophic Science, vol. , no. , 2021, pp. 87-95. DOI: https://doi.org/10.54216/IJNS.170201
    B., A. Broumi, S. A., L. (2021). n-Valued Refined Neutrosophic Crisp Sets. International Journal of Neutrosophic Science, (), 87-95. DOI: https://doi.org/10.54216/IJNS.170201
    B., Ahmed. Broumi, Said. A., Luay. n-Valued Refined Neutrosophic Crisp Sets. International Journal of Neutrosophic Science , no. (2021): 87-95. DOI: https://doi.org/10.54216/IJNS.170201
    B., A. , Broumi, S. , A., L. (2021) . n-Valued Refined Neutrosophic Crisp Sets. International Journal of Neutrosophic Science , () , 87-95 . DOI: https://doi.org/10.54216/IJNS.170201
    B. A. , Broumi S. , A. L. [2021]. n-Valued Refined Neutrosophic Crisp Sets. International Journal of Neutrosophic Science. (): 87-95. DOI: https://doi.org/10.54216/IJNS.170201
    B., A. Broumi, S. A., L. "n-Valued Refined Neutrosophic Crisp Sets," International Journal of Neutrosophic Science, vol. , no. , pp. 87-95, 2021. DOI: https://doi.org/10.54216/IJNS.170201

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