Continuous Pythagorean Fuzzy Set Extension with Multi-Attribute Decision Making Applications

OpenAlex İngilizce

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.