Some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision...

Area of Science:

• Fuzzy Mathematics
• Decision Science
• Information Theory

Background:

• Complex fuzzy sets (CFS) and probabilistic hesitant fuzzy sets (PHFS) handle specific types of uncertainty.
• Existing models may not adequately capture simultaneous randomness and ambiguity in real-world data.
• There is a need for advanced fuzzy set theory to address complex decision-making scenarios.

Purpose of the Study:

• To propose a novel fuzzy set, the complex probabilistic hesitant fuzzy set (CPHFS), integrating CFS and PHFS concepts.
• To develop fundamental operations and aggregation operators for CPHFS.
• To establish a multi-attribute decision-making (MADM) framework utilizing CPHFS.

Main Methods:

• Definition of complex probabilistic hesitant fuzzy elements (CPHFEs) and their basic operations.
• Development of aggregation operators: CPHFWA, CPHFWG, CPHFHM, CPHFGHM, and their weighted forms.
• Construction of a step-by-step MADM process within the CPHF environment.

Main Results:

• Established basic operations and operational laws for CPHFEs.
• Introduced novel aggregation operators that account for attribute interrelationships.
• Demonstrated the effectiveness of the proposed MADM process with a practical example (car purchasing).

Conclusions:

• The CPHFS effectively models complex decision-making information with simultaneous randomness and ambiguity.
• The proposed MADM method offers superior performance compared to existing approaches for interactive attributes.
• The framework provides a robust tool for addressing complex multi-attribute decision-making problems.