Supply chain management provides a significant aspect in enhancing competitive pressure, but the shift toward an ecological mentality has led to the emergence of green supplier selection. The problem of choosing environmentally friendly suppliers is discussed in this study, emphasizing sustainability, durability, agility, and ecological sensitivity. To assess green suppliers, with regard to the recycling, environmental applications, carbon footprint, and water consumption issues in T-spherical linear Diophantine fuzzy sets aspects, an integrated multi-criteria decision-making method has been employed. (T-SLDFS are effective in multi-criteria decision-making, covering data in two variable parameters and three parametric data.) The MCDM algorithm is built using a novel distance and an entropy measure, with integrated weights assessing criteria relevance. The Entropy measure is utilized to analyze objective criteria weights, while the Stepwise Weight Assessment Ratio Analysis methodology is employed to determine subjective criteria weights. To frame the Technique for Order of Preference by Similarity to Ideal Solution methodology for evaluating alternatives, the distance measure is adopted. The study evaluates the persistence and consistency of the proposed approach for assessing the hierarchy of preference of GSSs through comparison research and sensitivity analysis.