Developing an intuitionistic fuzzy rough new correlation coefficient approach for enhancing robotic vacuum cleaner

Area of Science:

• Decision Science
• Graph Theory
• Fuzzy Set Theory

Background:

• Intuitionistic fuzzy rough models integrate intuitionistic fuzzy sets and rough sets for complex uncertainty.
• Correlation coefficients are vital for assessing relationships in data, particularly within graph structures.

Purpose of the Study:

• To develop and apply a novel correlation coefficient for intuitionistic fuzzy rough graphs.
• To enhance attribute decision-making by integrating correlation coefficients into an intuitionistic fuzzy rough environment.
• To improve the handling of uncertainty and imprecision in decision-making processes.

Main Methods:

• Utilizing correlation coefficient and weighted correlation coefficient to measure relationships between intuitionistic fuzzy rough graphs.
• Calculating Laplacian energy and a new correlation coefficient for intuitionistic fuzzy rough graphs.
• Proposing an adjusted correlation coefficient for relative position load computation and ranking alternatives.

Main Results:

• A new approach for calculating correlation coefficients in intuitionistic fuzzy rough graphs is presented.
• The proposed method successfully ranks alternatives by comparing them to an ideal choice.
• The effectiveness is demonstrated through an example optimizing robotic vacuum cleaner decision-making.

Conclusions:

• The developed correlation coefficient method enhances decision-making in uncertain and imprecise environments.
• This approach offers a robust framework for attribute decision-making using intuitionistic fuzzy rough preference relations.
• The study provides a practical tool for optimizing complex systems through improved data analysis.