Abstract
Pythagorean cubic fuzzy is a relatively new improvement in the field of fuzzy set (FS) theory. It is a mathematical framework that allows decision-makers to effectively evaluate and select the best course of action when faced with uncertainty and ambiguity. The theory is built on the idea of a Pythagorean FS (PFS), which is a generality of the traditional FS. It also includes a cubical structure, which allows for more flexibility in representing complex relationships. The Pythagorean cubic fuzzy (PCF) sets (PCFSs) provide a way to model and handle uncertainty more precisely and accurately, giving decision-makers the ability to make better-informed decisions in uncertain and fuzzy environments. This study aims to investigate the use of Frank operations, which are a type of mathematical operation, to aggregate PCF numbers (PCFNs) and provide a powerful tool for decision-making in uncertain and fuzzy environments. We introduce new operations for PCF environments, including the Frank sum, product, scalar multiplication and exponentiation. Using these operations, we develop new a series of aggregation operators (AOs) such as the PCF Frank weighted averaging (PCFFWA) and PCF Frank weighted geometric (PCFFWG) operator. We establish various properties of these operators, provide examples of them, and examine the connections between these operators. Furthermore, we utilize these operators to devise a method for handling group decision-making with CPF information. To demonstrate the usefulness and efficiency of the operators and method, we present a numerical example. Finally, we compare the results of the proposed method with existing methods to demonstrate its applicability and feasibility.
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Rahim, M. Multi-criteria group decision-making based on frank aggregation operators under Pythagorean cubic fuzzy sets. Granul. Comput. 8, 1429–1449 (2023). https://doi.org/10.1007/s41066-023-00376-z
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DOI: https://doi.org/10.1007/s41066-023-00376-z