A Fermatean fuzzy MCDM method for selection and ranking Problems: Case studies

The fuzzy set theory has been evolving to represent the uncertainty in the real-world decision-making environment. Literature has been steadily expanding to incorporate subjective judgments and ambiguous information in the decision-making process, aiming to enhance the reliability and flexibility of data representation. Fermatean Fuzzy Sets (FFSs), a recent extension of intuitionistic fuzzy sets, address the limitations associated with membership functions and the representation of hesitation in multi-criteria decision-making (MCDM) methods. The aim of this study is to examine the performance of FFSs in exploiting uncertainty in selection and ranking decisions in MCDM problems. The performance of FFSs is investigated for Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) which is extended with Stepwise Weight Assessment Ratio Analysis (SWARA) method for criteria evaluations. This study is designed to present a comparative analysis for three different types of fuzzy set definitions: classical fuzzy sets with fuzzy triangular numbers, Intuitionistic Fuzzy Sets (IFSs), and FFSs, for MCDM problems under uncertainty. The proposed methodology is applied to two real case studies: (i) to rank Turkish research universities for performance assessment and (ii) to select the optimal facility location for a company in the beverage industry. To assess the effectiveness of the FFSs in multiple criteria selection and ranking decisions, a comparative analysis is conducted on two real-world problems. The results show that FFSs provide valuable insight especially for multiple criteria ranking problems. The comparative analysis highlights the effectiveness of Fermatean Fuzzy SWARA-TOPSIS method and its potential for practical ranking applications.