Intuitionistic fuzzy approach based on correlation coefficient and signless Laplacian energy with applications

Decision-making in uncertain and complex environments requires methods that can effectively capture ambiguity in expert judgments. Traditional fuzzy graph models often overlook non-membership and hesitation degrees, limiting their descriptive power. To address this limitation, we propose a novel group decision-making framework based on intuitionistic fuzzy graphs (IFG’s), integrating Signless Laplacian energy ([Formula: see text]) with a correlation coefficient ([Formula: see text]) measure. In the proposed model, [Formula: see text] is used to derive objective criterion weights, while [Formula: see text] evaluates the similarity among alternatives. Two complementary procedures ensure consistent and robust rankings. The framework is validated through a case study on electric vehicle selection, considering alternatives based on range, safety, and price. Results show that both procedures produce identical rankings and improve decision consistency compared with existing methods using only [Formula: see text] or [Formula: see text]. This demonstrates that the unified framework reduces ambiguity, enhances ranking reliability, and provides practical support for sustainable technology adoption under uncertainty.