International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 20 , Issue 2 , PP: 107-134, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

A new type of neutrosophic set in Pythagorean Fuzzy environment and Applications to multi-criteria decision making

Mahmut Can Boziygit 1 * , Murat Olgun 2 , Florentin Smarandache 3 , Mehmet Unver 4

  • 1 Ankara Yildirim Beyazit University, Faculty of Engineering and Natural Sciences, Department of Mathematics, 06420 Ankara, Turkey - (munver@ankara.edu.tr)
  • 2 Ankara University, Faculty of Science, Department of Mathematics, 06100 Ankara, Turkey - (olgun@ankara.edu.tr)
  • 3 Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA - (smarand@unm.edu)
  • 4 Ankara University, Faculty of Science, Department of Mathematics, 06100 Ankara Turkey - (munver@ankara.edu.tr)
  • Doi: https://doi.org/10.54216/IJNS.200208

    Received: July 08, 2022 Accepted: January 11, 2023
    Abstract

    In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. First of all, we propose the concepts of Pythagorean fuzzy t-norm and t-conorm and show that some Pythagorean fuzzy t-norms and t-conorms are expressed via ordinary continuous Archimedean tnorms and t-conorms. Then we define the concepts of PFVNS and PFVNV and provide a tool to construct a PFVNV from an ordinary neutrosophic fuzzy value. We also define some set theoretic operations between PFVNSs and some algebraic operations between PFVNVs via t-norms and t-conorms. With the help of these algebraic operations we propose some weighted aggregation operators. To measure discrimination information of PFVNVs, we define a simplified neutrosophic valued modified fuzzy cross-entropy measure. Moreover, we introduce a multi-criteria decision making method in Pythagorean fuzzy valued neutrosophic environment and practice the proposed theory to a real life multi-criteria decision making problem. Finally, we study the comparison analysis and the time complexity of the proposed method.

    Keywords :

    Pythagorean fuzzy valued neutrosophic set , aggregation operators , multi-criteria decision making

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    Cite This Article As :
    Can, Mahmut. , Olgun, Murat. , Smarandache, Florentin. , Unver, Mehmet. A new type of neutrosophic set in Pythagorean Fuzzy environment and Applications to multi-criteria decision making. International Journal of Neutrosophic Science, vol. , no. , 2023, pp. 107-134. DOI: https://doi.org/10.54216/IJNS.200208
    Can, M. Olgun, M. Smarandache, F. Unver, M. (2023). A new type of neutrosophic set in Pythagorean Fuzzy environment and Applications to multi-criteria decision making. International Journal of Neutrosophic Science, (), 107-134. DOI: https://doi.org/10.54216/IJNS.200208
    Can, Mahmut. Olgun, Murat. Smarandache, Florentin. Unver, Mehmet. A new type of neutrosophic set in Pythagorean Fuzzy environment and Applications to multi-criteria decision making. International Journal of Neutrosophic Science , no. (2023): 107-134. DOI: https://doi.org/10.54216/IJNS.200208
    Can, M. , Olgun, M. , Smarandache, F. , Unver, M. (2023) . A new type of neutrosophic set in Pythagorean Fuzzy environment and Applications to multi-criteria decision making. International Journal of Neutrosophic Science , () , 107-134 . DOI: https://doi.org/10.54216/IJNS.200208
    Can M. , Olgun M. , Smarandache F. , Unver M. [2023]. A new type of neutrosophic set in Pythagorean Fuzzy environment and Applications to multi-criteria decision making. International Journal of Neutrosophic Science. (): 107-134. DOI: https://doi.org/10.54216/IJNS.200208
    Can, M. Olgun, M. Smarandache, F. Unver, M. "A new type of neutrosophic set in Pythagorean Fuzzy environment and Applications to multi-criteria decision making," International Journal of Neutrosophic Science, vol. , no. , pp. 107-134, 2023. DOI: https://doi.org/10.54216/IJNS.200208