Fermatean Hesitant Fuzzy Sets for Multiple Criteria Decision-Making with Applications

The Fermatean hesitant fuzzy set idea obtained by combining Fermatean fuzzy sets and hesitant fuzzy sets can be used in practice to simplify the solution of complicated multi-criteria decision-making problems. Initially, the notion of a Fermatean hesitant fuzzy set has been given, and the operations related to this concept have been presented. The basic properties of aggregation operators based on Fermatean hesitant fuzzy sets have been studied. To choose the best alternative in practice, a novel multi-criteria decision-making method that is obtained with operators has been created. Finally, numerical examples were examined to indicate the effectiveness of the suggested techniques. The main advantages of this work include three points: (1) extending hesitant fuzzy sets to the Fermatean fuzzy case and proposing two types of aggregation operators for the Fermatean hesitant fuzzy information; (2) considering the interaction among decision-makers and among attributes in decision problems, and dealing with this interrelationship by fuzzy measure; (3) introducing the new decision method for the Fermatean hesitant fuzzy environment and enriching the mathematical tools to solve multiple attributes decision-making problems.