Einstein aggregation operators for multicriteria group decision making in uncertain environments using cubic picture fuzzy sets

This research presents an in-depth study of various operational laws, Einstein operations, and novel aggregation strategies for handling cubic picture fuzzy data. We developed and presented three new arithmetic averaging operators. These operators are called cubic picture fuzzy Einstein weighted averaging (CPFEWA), cubic picture fuzzy Einstein ordered weighted averaging (CPFEOWA), and cubic picture fuzzy Einstein hybrid weighted averaging (CPFEHWA). These operators have been designed to provide more precise and accurate calculations for arithmetic averaging. Particularly, the CPFEHWA operator extends the capabilities of both CPFEWA and CPFEOWA operators. To gain a better understanding, we thoroughly investigate the features of these operators and connect them to existing aggregate operators. We show how these innovative Einstein operators can be useful and expose their derived operators, such as CIFEWA, CFEWA, PFEWA, CIFEOWA, CFEOWA, PFEOWA, CIFEHWA, CFEHWA, and PFEHWA. We developed three properties of these operators as idempotency, monotonicity and boundedness. Furthermore, we show how the CPFEHWA operator may be used in multiple attribute decision-making (MADM) scenarios employing cubic picture fuzzy data. The new insights gained from this study are valuable as they offer innovative ways of collecting and interpreting cubic picture fuzzy data. This adds to the existing knowledge base, making it easier to understand and use in future research. We propose an informative set of tools for decision-making processes involving complex and unreliable data, presenting the CPFEWA, CPFEOWA, and CPFEHWA operators. A numerical example demonstrating the application of the CPFEHWA operator in a real-life setting is provided to demonstrate the effectiveness of our suggested concept. This example's results support the proposed methodology and illustrate its potential significance in practical applications.