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A New Approach to Neutrosophic Soft Mappings and Application in Decision Making

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Neutrosophic Operational Research

Abstract

Samarandache introduced the neutrosophic set concept in 1995 to solve uncertainty data. After that, Maji introduced the concept of neutrosophic soft set by combining the neutrosophic sets and soft sets as a general mathematical tool. Due to some structural deficiencies in Maji’s study, Ozturk et al. re-defined some operations on neutrosophic soft sets. The neutrosophic soft mapping was firstly defined by Alkhazaleh et al. However, Alkhazaleh’s study does not provide some basic classical mapping properties and it has structural problems. For that reason, we propose a new approach to neutrosophic soft mapping. In this study, we re-define neutrosophic soft mappings and studied the images and inverse images of neutrosophic soft sets. Further, we investigate the basic operations and other related properties of neutrosophic soft mappings. Finally, the neutrosophic soft mapping have been applied to application in decision making.

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References

  1. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

    Article  Google Scholar 

  2. Smarandache, F. (2005). Neutrosophic set, a generalisation of the intuitionistic fuzzy sets. International Journal of Pure and Applied Mathematics, 24, 287–297.

    Google Scholar 

  3. Atanassov, K. T. (1999). Intuitionistic fuzzy sets (pp. 1–137). Heidelberg: Physica.

    Book  Google Scholar 

  4. Abobala, M. (2020). On Some Special Substructures of Refined Neutrosophic Rings. International Journal of Neutrosophic Science, 5(1), 59–66.

    Google Scholar 

  5. Ansari, A. Q., Biswas, R., & Aggarwal, S. (2011). Proposal for applicability of neutrosophic set theory in medical AI. International Journal of Computer Applications, 27(5), 5–11.

    Article  Google Scholar 

  6. Gallego Lupiáñez, F. (2008). On neutrosophic topology. Kybernetes, 37(6), 797–800.

    Article  Google Scholar 

  7. Hatip, A. (2020). The special neutrosophic functions. International Journal of Neutrosophic Science, 4(2), 104–116.

    Google Scholar 

  8. Kharal, A. (2014). A neutrosophic multi-criteria decision making method. New Mathematics and Natural Computation, 10(02), 143–162.

    Article  Google Scholar 

  9. Nandhini, T., & Vigneshwaran, M. (2020). On neutrosophic nano αg#ψ-closed sets in neutrosophic nano topological spaces. International Journal of Neutrosophic Science, 5(2), 67–71.

    Google Scholar 

  10. Nordo, G., Mehmood, A., & Broumi, S. (2020). Single valued neutrosophic filters. International Journal of Neutrosophic Science, 6(1), 08–21.

    Google Scholar 

  11. Ozturk, T. Y., & Ozkan, A. (2019). Neutrosophic bitopological spaces. Neutrosophic Sets and Systems, 88, 97–106.

    Google Scholar 

  12. Molodtsov, D. (1999). Soft set theory-first results. Computers & Mathematcs with Applications, 37, 19–31.

    Article  Google Scholar 

  13. Feng, F., Li, C., Davvaz, B., & Ali, M. I. (2010). Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Computing, 14(9), 899–911.

    Article  Google Scholar 

  14. Kharal, A., & Ahmad, B. (2009). Mappings on fuzzy soft classes. Adv. Fuzzy Syst., 2009, 407890, 6 pages.

    Google Scholar 

  15. Ozturk, T. Y. (2018). On bipolar soft topological spaces. Journal of New Theory, 20, 64–75.

    Google Scholar 

  16. Yin, Y., Li, H., & Jun, Y. B. (2012). On algebraic structure of intuitionistic fuzzy soft sets. Computers and Mathematics with Applications, 64(9), 2896–2911.

    Article  Google Scholar 

  17. Maji, P. K. (2013). Neutrosophic soft set, Ann. Fuzzy Mathematics and Informatics, 5(1), 157–168.

    Google Scholar 

  18. Ozturk, T., Gunduz Aras, C., & Bayramov, S. (2019). A new approach to operations on neutrosophic soft sets and to neutrosophic soft topological spaces. Communications in Mathematics and Applications, 10(3), 481–493. https://doi.org/10.26713/cma.v10i3.1068.

    Article  Google Scholar 

  19. Bera, T., & Mahapatra, N. K. (2017). Introduction to neutrosophic soft topological space. Opsearch, 54(4), 841–867.

    Article  Google Scholar 

  20. Bera, T., & Mahapatra, N. K. (2016). On neutrosophic soft function. Ann. Fuzzy Math. Inform., 12(1), 101–119.

    Google Scholar 

  21. Deli, I., & Broumi, S. (2015). Neutrosophic soft relations and some properties, Ann. Fuzzy Mathematics and Informatics, 9(1), 169–182.

    Google Scholar 

  22. Gunduz, C., Ozturk, T. Y., & Bayramov, S. (2019). Separation axioms on neutrosophic soft topological spaces. Turkish Journal of Mathematics, 43(1), 498–510.

    Article  Google Scholar 

  23. Ozturk, T. Y., & Simsekler (Dizman), T. (2019). A new approach to operations on bipolar neutrosophic soft sets and bipolar neutrosophic soft topological spaces. Neutrosophic Sets & Systems, 30, 31–42.

    Google Scholar 

  24. Kharal, A., & Ahmad, B. (2011). Mappings on soft classes. New Mathematics and Natural Computation, 7(03), 471–481.

    Article  Google Scholar 

  25. Alkhazaleh, S., & Marei, E. (2014). Mappings on neutrosophic soft classes. Neutrosophic Sets and Systems, 2, 3–8.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematic, Kafkas University, Kars, Turkey

    Adem Yolcu, Elif Karatas & Taha Yasin Ozturk

Authors
  1. Adem Yolcu
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  2. Elif Karatas
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  3. Taha Yasin Ozturk
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Corresponding author

Correspondence to Adem Yolcu .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Science, University of New Mexico, Gallup, NM, USA

    Florentin Smarandache

  2. Faculty of Computers and Informatics, Zagazig University, Zagazig, Sharqiyah, Egypt

    Mohamed Abdel-Basset

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Yolcu, A., Karatas, E., Ozturk, T.Y. (2021). A New Approach to Neutrosophic Soft Mappings and Application in Decision Making. In: Smarandache, F., Abdel-Basset, M. (eds) Neutrosophic Operational Research. Springer, Cham. https://doi.org/10.1007/978-3-030-57197-9_15

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