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

Area of Science:

• Fuzzy Set Theory
• Decision Sciences
• Information Fusion

Background:

• Handling complex and uncertain data is crucial in modern decision-making.
• Existing aggregation operators may lack the precision needed for cubic picture fuzzy environments.
• There is a need for advanced tools to manage and analyze multi-dimensional fuzzy information.

Purpose of the Study:

• To develop and investigate new arithmetic averaging operators for cubic picture fuzzy data.
• To introduce cubic picture fuzzy Einstein weighted averaging (CPFEWA), Einstein ordered weighted averaging (CPFEOWA), and Einstein hybrid weighted averaging (CPFEHWA) operators.
• To demonstrate the applicability of these operators in multiple attribute decision-making (MADM) scenarios.

Main Methods:

• Development of three novel Einstein averaging operators: CPFEWA, CPFEOWA, and CPFEHWA.
• Analysis of operator properties including idempotency, monotonicity, and boundedness.
• Application of the CPFEHWA operator in a multiple attribute decision-making (MADM) framework using cubic picture fuzzy data.

Main Results:

• The proposed CPFEWA, CPFEOWA, and CPFEHWA operators provide precise arithmetic averaging for cubic picture fuzzy data.
• The CPFEHWA operator is shown to be a versatile extension of CPFEWA and CPFEOWA.
• Demonstrated effectiveness of the CPFEHWA operator through a numerical example in a real-life MADM context.

Conclusions:

• The novel Einstein operators offer significant advancements in handling cubic picture fuzzy data.
• These operators provide valuable tools for decision-making processes involving complex and uncertain information.
• The research contributes innovative methods for collecting and interpreting cubic picture fuzzy data, enhancing future research and practical applications.