The problem and complication arise from the growing environmental inefficiencies and concerns in traditional supply chains, for instance, poor accountability, excessive waste, and lack of transparency. The green supply chain practices aim to reduce or minimize the environmental impact of supply chain activities, but these efforts often face problems, for example, difficulty in monitoring sustainability performance, data manipulation, and limited traceability across numerous stakeholders. The main problem is that without effective techniques to verify and track eco-friendly practices, enterprises struggle to utilize and enforce green initiatives reliably. The blockchain technique is being derived as a solution because of its capability to give decentralized, transparent, and immutable records of processes and transactions. By integrating the blockchain into green supply chain practices, we aim to design the model of linguistic (p, q)-rung orthopair fuzzy Z-number sets with algebraic and Sugeno-Weber operational laws for the construction of the power weighted averaging operator and power weighted geometric operator. These operators can be used in the utilization of the multi-attributive border approximation area comparison model, which is also explained step-by-step with the help of examples to simplify the supremacy and validity of the invented model by comparing their ranking values with the ranking values of the existing approaches.