Fermatean Fuzzy Analytic Hierarchy Process for Supplier Selection on LARG Supply Chain Paradigm

Abstract

Multi-criteria decision-making (MCDM) methods have proven to be successful at solving complex decision problems. The fuzzy set theory, recognized for its ability to capture and represent uncertainty in real-world problems, has been extensively incorporated. Within the MCDM method literature, various fuzzy sets have been created to manage uncertain information inherent in real-world decision-making processes. Fermatean Fuzzy Sets (FFS), an extension of intuitionistic fuzzy sets (IFS), emerge as a robust framework for addressing uncertainty challenges in real-world problems. FFSs, demonstrating enhanced capabilities in mitigating limitations associated with membership functions and effectively representing hesitancy, contribute significantly to advancing MCDM methodologies. One of the most critical MCDM problems is supplier selection. Recently, supply chains have become vulnerable due to risks arising from various internal and external factors. Companies are striving to increase their supply chain performance in a competitive, risky, and ever-changing environment by adopting different paradigms. In this context, the integration of lean, agile, resilient, and green (LARG) paradigms into supply chains serves to elevate the operational performance and strategic competitiveness of these companies. Determining the most suitable supplier group is an important decision-making process crucial for the successful pursuit of integrated supply chain paradigms. This paper aims to provide a comparative examination for distinct types of fuzzy set definitions: Spherical fuzzy sets (SFS), IFSs, and FFSs for MCDM problems involving uncertainty. To test the performance of the FFSs in solving real-world problems, a comparative analysis is applied in a case study using the FF-AHP (Analytic Hierarchy Process) method.