A strategic decision-making framework for evaluating barriers to green supply chain management using fractional fuzzy similarity measures

The study of similarity and distance measures plays a key role in understanding the relationships between fuzzy sets and their extensions, especially when applied to decision-making problems. While there has been notable progress in developing similarity measures for various types of generalized fuzzy sets, including fractional fuzzy sets, there is still a lack of well-developed measures suited to the structure of [Formula: see text]fractional fuzzy sets. This limitation reduces the effectiveness of fuzzy models in complex decision-making tasks where uncertainty needs to be handled more carefully and flexibly. To overcome this issue, we introduce new similarity measures that use three independent fractional exponents [Formula: see text], [Formula: see text], and [Formula: see text] corresponding to the membership, neutral, and non-membership degrees. This approach offers greater flexibility and a more detailed way of capturing the relationships between fuzzy values. We also apply these similarity measures within a decision-making model designed to assess alternatives in uncertain environments. The proposed method is tested through a multi-criteria decision-making case study. The results highlight that regulatory and policy barriers ([Formula: see text]​) are the most influential factor, with a final score of [Formula: see text], showing the method's usefulness in real-world settings. Compared to other approaches, our framework adapts better to changes in uncertainty, responds more accurately to variations in input values, and offers clearer, more interpretable results.