Novel multiple criteria decision-making analysis under m-polar fuzzy aggregation operators with application

Area of Science:

• Decision Sciences
• Fuzzy Mathematics
• Operations Research

Background:

• Aggregation operators are crucial for simplifying multiple inputs into a single output for decision-making.
• M-polar fuzzy (mF) sets handle multipolar information, with existing aggregation tools like Dombi and Hamacher operators.
• A gap exists in aggregating m-polar fuzzy information using Yager's operations (t-norm and t-conorm).

Purpose of the Study:

• To introduce novel averaging and geometric aggregation operators for m-polar fuzzy information utilizing Yager's operations.
• To investigate the properties of these new operators, including boundedness, monotonicity, idempotency, and commutativity.
• To develop and apply a new algorithm for multi-criteria decision-making (MCDM) problems within an mF Yager environment.

Main Methods:

• Development of mF Yager weighted averaging (mFYWA) and mF Yager weighted geometric (mFYWG) operators, along with their ordered and hybrid variants.
• Mathematical analysis of the proposed operators' fundamental properties.
• Formulation of an MCDM algorithm based on the mFYWA and mFYWG operators.
• Application of the developed operators to a real-world oil refinery site selection problem.

Main Results:

• Introduction of six new mF Yager aggregation operators (averaging and geometric types).
• Demonstration of the operators' properties through illustrative examples.
• Successful application of a novel MCDM algorithm using mFYWA and mFYWG operators in an oil refinery case study.
• Validation of the proposed operators' effectiveness and reliability through comparisons and existing tests.

Conclusions:

• The newly developed mF Yager aggregation operators effectively handle multipolar fuzzy information in MCDM.
• The proposed operators offer a valuable alternative to existing mF Dombi and Hamacher operators, particularly when Yager's operations are preferred.
• The real-world application demonstrates the practical utility and robustness of the new aggregation tools for complex decision-making scenarios.