A Novel Multi-Attribute Decision-Making Method Based on Linguistic Fermatean Fuzzy Sets and Power Average Operator

This chapter presents a novel multi-attribute decision-making (MADM) method based on linguistic Fermatean fuzzy sets (LFFSs) and power average operators. The method extends the existing Fermatean fuzzy sets (FFSs) to accommodate more complex decision-making environments. The chapter begins by reviewing basic concepts and definitions of FFSs and LFFSs, including operational rules, distance measures, and comparison methods. It then introduces new aggregation operators specifically designed for LFFSs, such as the linguistic Fermatean fuzzy power average (LFFPA) and power weighted average (LFFPWA) operators, and discusses their properties. The main contribution of the chapter is a new MADM method that leverages these operators to aggregate decision-makers' evaluations and determine the optimal alternative. An illustrative example is provided to demonstrate the effectiveness of the proposed method in a real-world software systems selection problem. The chapter concludes by highlighting the advantages of the new method and suggesting future research directions.