<p>This selection of environmentally sustainable suppliers is a critical and challenging task in green supply chain management due to the presence of uncertainty, subjectivity, and interaction among evaluation criteria. Multicriteria group decision-making methods are widely used for supplier selection; however, the reliability of experts’ judgments and handling of linguistic hesitation remain significant concerns. To address these issues, this study introduces fractional linguistic fuzzy sets, which provide a more flexible framework for representing experts’ assessments through linguistic membership and non-membership information. A novel score function and distance measure for fractional linguistic fuzzy numbers are developed to enhance discrimination among alternatives. Furthermore, several aggregation operators are proposed, including the fractional linguistic partitioned geometric Heronian mean, fractional linguistic fuzzy interactional weighted partitioned geometric Heronian mean, and fractional linguistic fuzzy interactional partitioned geometric Heronian mean operators, along with their fundamental properties. To improve ranking accuracy, a new grey relational analysis method is extended under the fractional fuzzy environment. The proposed approach is applied to a green supplier selection problem to demonstrate its practicality and effectiveness. Comparative analysis with existing methods confirms the robustness and reliability of the proposed decision-making framework.</p>