Interval-valued intuitionistic fuzzy MADM method based on TOPSIS and grey correlation analysis.

Area of Science:

• Decision Sciences
• Fuzzy Systems
• Operations Research

Background:

• Multi-Attribute Decision Making (MADM) often involves imprecise or uncertain information.
• Traditional methods struggle with fuzzy and rough data, leading to potential inaccuracies.
• Interval-valued intuitionistic fuzzy numbers offer a robust framework for handling such data.

Purpose of the Study:

• To develop an interval-valued intuitionistic fuzzy MADM method.
• To enhance decision-making objectivity and reasonableness when dealing with imprecise information.
• To integrate improved TOPSIS and Grey Correlation Analysis (GCA) for robust ranking.

Main Methods:

• Introducing interval intuitionistic fuzzy entropy to calculate attribute weights.
• Combining entropy and subjective weights for a comprehensive attribute weighting.
• Constructing absolute Positive Ideal Solution (PIS) and Negative Ideal Solution (NIS) to resolve TOPSIS's reverse order phenomenon.
• Integrating improved TOPSIS with GCA to determine alternative rankings.

Main Results:

• The proposed method effectively handles interval-valued intuitionistic fuzzy numbers in MADM.
• The integration of improved TOPSIS and GCA overcomes limitations of traditional methods.
• Sensitivity analysis confirms the rationality and effectiveness of the developed approach.
• The method provides a more objective and reasonable solution for MADM problems.

Conclusions:

• The novel interval-valued intuitionistic fuzzy MADM method offers a significant advancement.
• The approach enhances the reliability of decision-making in complex, uncertain environments.
• This research provides a valuable tool for selecting alternatives based on imprecise data.