A novel approach to MADM problems using Fermatean fuzzy Hamacher aggregation operators

The intuitionistic fuzzy set, briefly as; IFS and its extension involving Pythagorean fuzzy set (PFS) and Fermatean fuzzy set (FFS), are all effective tools to express uncertain and incomplete cognitive information with membership, nonmembership, and hesitancy degrees. The FFS introduced by Senapati and Yager, carries out uncertain and imprecise information smartly in exercising decision-making than IFS and PFS. A generalized form of union and intersection on FFS can be formulated from a generalized T-norm and T-conorm. Hamacher operations such as Hamacher product and Hamacher sum, are good alternatives to product and sum. In this course of this article, we first device new operations on Fermatean fuzzy information by employing Hamacher T-conorm and T-norm and discuss basic operations. Induced by the Hamacher operations and FFS, we propose Fermatean fuzzy Hamacher arithmetic and also geometric aggregation operators. In the first section, we introduce the concepts of a Fermatean fuzzy Hamacher weighted average operator, a Fermatean fuzzy Hamacher ordered weighted average operator, and a Fermatean fuzzy Hamacher hybrid weighted operator and discuss their basic properties in detail. In the second part, we develop Fermatean fuzzy Hamacher weighted geometric operator, Fermatean fuzzy Hamacher ordered weighted geometric operator, and Fermatean fuzzy Hamacher hybrid geometric operator. We study essential properties and a few special cases of our newly introduced operators. Then, we make use of these proposed operators in developing tools which are key factors in solving the Fermatean fuzzy multiattribute decision-making situations. The cyclone disaster assessment phenomena is considered as a direct application for analysis and to demonstrate the practicality and efficacy of our model. Further, comparison analysis is conducted for the authenticity of our proposed operators.

Automated summary

The article introduces the intuitionistic fuzzy set, Pythagorean fuzzy set, and Fermatean fuzzy set as tools for expressing uncertain and incomplete information, discussing their applications in decision-making. New operations on Fermatean fuzzy information are devised using Hamacher norms, proposing Fermatean fuzzy Hamacher arithmetic and geometric aggregation operators. A direct application in cyclone disaster assessment is used to demonstrate the efficacy of the model and comparison analysis is conducted for authenticity.