An enhanced VIKOR method for multi-criteria group decision-making with complex Fermatean fuzzy sets

Area of Science:

• Decision Sciences
• Fuzzy Set Theory
• Operations Research

Background:

• Conventional decision-making methods struggle with complex, multi-dimensional uncertain data.
• Fermatean fuzzy sets and N-soft sets offer enhanced capabilities for handling imprecision.
• The VIKOR method is a robust technique for identifying compromise solutions in decision-making.

Purpose of the Study:

• To propose a novel decision-making approach, the complex Fermatean fuzzy N-soft VIKOR method.
• To extend the applicability of the VIKOR method to complex Fermatean fuzzy N-soft environments.
• To address multi-attribute group decision-making challenges with uncertain and multi-valued information.

Main Methods:

• Amalgamation of complex Fermatean fuzzy N-soft set theory with the VIKOR decision-making technique.
• Assignment of N-soft grades to decision-makers, alternatives, and attributes.
• Utilization of a complex Fermatean fuzzy N-soft weighted average operator for opinion aggregation.
• Conversion of aggregated data to crisp values using a score function for ranking.

Main Results:

• Development of a technique for ranking alternatives based on group utility and individual regret.
• Successful application of the method to select the optimal location for a nuclear power plant.
• Demonstration of the method's accuracy and veracity through comparative analysis with Fermatean fuzzy TOPSIS.

Conclusions:

• The proposed complex Fermatean fuzzy N-soft VIKOR method provides an effective framework for complex decision-making.
• The method enhances the handling of multi-dimensional uncertain information in group decision scenarios.
• Further research can explore the limitations and expand the applications of this integrated approach.