Continuous Pythagorean Fuzzy Set Extension with Multi-Attribute Decision Making Applications
Volume 36, Issue 2 (2025), pp. 241–283
Pub. online: 28 January 2025
Type: Research Article
Open Access
Open Access
Received
1 July 2024
1 July 2024
Accepted
1 January 2025
1 January 2025
Published
28 January 2025
28 January 2025
Abstract
One of the most recent innovations in the field of fuzzy sets has been continuous intuitionistic fuzzy sets (CINFUSs), where membership and non-membership degrees are defined by nonlinear functions, as a direct extension of intuitionistic fuzzy sets (IFSs). The membership and non-membership degrees of CINFUSs can account for uncertainty at every point since they are represented by continuous structures that change based on how the decision-maker responds to uncertainty. On the other hand, Pythagorean fuzzy sets (PFSs) allow for a more accurate representation of the data and a better way to handle uncertainty in decision issues by reflecting the hesitations of decision-makers over a larger range. Due to these superior advantages of CINFUSs and the fact that PFSs are more comprehensive than IFSs, in this study, continuous Pythagorean fuzzy sets (CPFUSs) have been aimed at introducing to define uncertainty more broadly and accurately by representing PFSs with a continuous structure as in IFSs. In this study, firstly, the basic principles and mathematical operators of CPFUSs have been developed and presented. Then, multi-attribute decision-making (MADM) models have been developed by considering different aggregation operators to indicate the feasibility and effectiveness of the continuous Pythagorean fuzzy (CPFU) extension. The developed CPFU-MADM models have been implemented to the solution of two different decision problems: green supplier selection and waste disposal site selection problems. In addition, sensitivity analyses have been conducted on criterion weights, expert weights and parameters in order to demonstrate the reliability and stability of the developed models. Furthermore, the validity and superiority of the developed models have been indicated by the comparative analysis conducted with IFSs and PFSs-based MADM models in the literature. MADM applications have shown that continuous Pythagorean fuzzy sets can successfully represent the expert decisions with different attitudes within the same model. It has been observed that the rankings of alternatives according to aggregation operators do not change even when there are differences in the score values of the alternatives.
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Biographies
Alkan Nurşah
N. Alkan is a PhD candidate in the Department of Industrial Engineering at Istanbul Technical University since 2019. She received the MSc degree in Department of Industrial Engineering from Yildiz Technical University, Turkey, in 2019. Her research interests include fuzzy sets and their extensions, multi-criteria/objective decision making, and data analysis. She published some journal papers, conference papers and book chapters in mentioned areas.
Kahraman Cengiz
C. Kahraman is a full professor at Istanbul Technical University. His research areas are engineering economics, quality management, statistical decision making, multicriteria decision making, and fuzzy decision making. He published about 300 international journal papers and about 200 conference papers. He became the guest editor of many international journals and the editor of many international books from Springer. He is a member of editorial boards of 20 international journals. He is the chair of INFUS International Conferences on fuzzy and intelligent systems.
