International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1527 2020 2020 Ankara Yildirim Beyazit University, Faculty of Engineering and Natural Sciences, Department of Mathematics, 06420 Ankara, Turkey Mahmut Can Boziygit Ankara University, Faculty of Science, Department of Mathematics, 06100 Ankara, Turkey Murat Olgun Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA Florentin Smarandache Ankara University, Faculty of Science, Department of Mathematics, 06100 Ankara Turkey Mehmet Unver 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. 2023 2023 107 134 10.54216/IJNS.200208 https://www.americaspg.com/articleinfo/21/show/1527