A new definition for quartic fuzzy sets with hesitation grade applied to multi-criteria decision-making problems under uncertainty

Pythagorean fuzzy sets and Fermatean fuzzy sets are used to enhance the flexibility of intuitionistic fuzzy sets for decision-making under uncertainty in fuzzy environments. This study presents and compares a new definition of quartic fuzzy sets with intuitionistic, Pythagorean, and Fermatean fuzzy sets. In addition, we study set operations, score function, and accuracy function of the quartic fuzzy sets. Euclidean distance and similarity measures for quartic fuzzy sets are proposed, which will help solve many real-life problems under uncertainty. We then develop an algorithm to tackle the problem of multiple criteria decision-making. A comparison of the novel quartic fuzzy sets with the existing intuitionistic, Pythagorean, and Fermatean fuzzy sets is provided to demonstrate the advantages of the proposed quartic fuzzy sets. Finally, a practical example is presented to demonstrate the applicability and efficacy of the proposed fuzzy sets. The results of the study indicate that new definition of quartic fuzzy sets produce the most consistent and reliable ranking for handling uncertain and indeterminate information.