Complex nth power root fuzzy sets: Theory, and applications for multi-attribute decision making in uncertain...

Area of Science:

• Fuzzy Set Theory
• Decision Making
• Uncertainty Quantification

Background:

• Traditional fuzzy sets struggle with complex ambiguity.
• Intuitionistic and Pythagorean fuzzy sets offer improvements but have limitations.
• Nth power root fuzzy sets enhance ambiguity management.

Purpose of the Study:

• To introduce and explore complex nth power root fuzzy sets (CnPR-FSs).
• To integrate nth power root fuzzy sets with complex fuzzy sets.
• To demonstrate the superiority of CnPR-FSs in representing uncertainty.

Main Methods:

• Integration of nth power root fuzzy sets and complex fuzzy sets.
• Development of a constraint for CnPR-FSs to represent broader uncertainty.
• Creation of comparison, accuracy, and scoring functions for complex nth power root fuzzy numbers.
• Introduction of novel aggregation operators: CnPR-FWA and CnPR-FWG.

Main Results:

• CnPR-FSs provide a more effective way to describe uncertain data than complex intuitionistic and Pythagorean fuzzy sets.
• The proposed constraint broadens the representation of uncertain information.
• Customized functions and novel aggregation operators enhance decision-making capabilities.
• The method was successfully applied to selecting a caterer and venue for corporate events.

Conclusions:

• CnPR-FSs are a powerful tool for managing ambiguity and vagueness in complex decision-making scenarios.
• The developed framework offers practical advantages over existing methods.
• The study highlights the efficacy and applicability of CnPR-FSs in real-world decision problems.