Branch Mathematics and Statistics Faculty and Staff Publications
Document Type
Article
Publication Date
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 t-norms 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 informaIntion 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.
Publication Title
International Journal of Neutrosophic Science
Language (ISO)
English
Keywords
Pythagorean fuzzy valued neutrosophic set; aggregation operators; multi-criteria decision making
Recommended Citation
Bozyıgıt, Mahmut Can; Murat Olgun; Florentin Smarandache; and Mehmet Unver. "A New Type of Neutrosophic Set in Pythagorean Fuzzy Environment and Applications to Multi-criteria Decision Making." International Journal of Neutrosophic Science (2023). https://digitalrepository.unm.edu/math_fsp/596
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
