Transporting goods is crucial to both the production sector and daily life. It provides essential supplies for technological and manufacturing processes as well as supplies for human consumption. However, cars have a big impact on the environment. Monitoring transportation use is essential, as is promoting the use of technology, cars, and fuels that are environmentally benign. The most urgent problem facing all parties involved in urban freight transportation is this one. In order to address this significant issue, this paper suggests a two-stage multi-attribute decision-making (MADM) technique based on the interval-valued \(q-\) rung orthopair fuzzy (IV \(q-\) ROF) strategy. The IV \(q-\) ROFSs, an extension of fuzzy sets, expands on the idea of q-rung orthopair fuzzy sets by enabling the representation of membership and non-membership degrees as intervals as opposed to single values. This gives decision-makers greater freedom to communicate their choices, particularly in the face of ambiguity and uncertainty. To aggregate the evaluation data for goods transportation decision-making, IV \(q-\) ROF Hamacher interactive operators are defined in the initial phase that is dependent on the Hamacher operations. The IV \(q-\) ROF Hamacher interactive weighted averaging (IV \(q-\) ROFHIWA), IV \(q-\) ROF Hamacher interactive ordered weighted average (IV \(q-\) ROFHIOWA), and IV \(q-\) ROF Hamacher interactive hybrid weighted average (IV \(q-\) ROFHIHWA) operators are specifically constructed and proven. Additionally, consistency, boundedness, and monotonicity are among the proposed operators’ qualities that are stated and demonstrated. The optimal vehicle for goods transportation is chosen in the second stage using a MADM technique under the IV \(q-\) ROF environment that depends on the IV \(q-\) ROFHIWA operator. Finally, a comparison and sensitivity perusals have been used to validate the accuracy and superiority of the developed technique.
