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Abstract The linguistic q-rung orthopair fuzzy ( $$L^{q}ROF$$ L q R O F ) set serves as a useful way of presenting uncertain information by offering more space for decision experts. In the present research, we first link the concepts of Hamacher t-norm and t-conorm with the frame of $$L^{q}ROF$$ L q R O F numbers to develop and analyze the innovative $$L^{q}ROF$$ L q R O F Hamacher operations. Then, following the proposed Hamacher’s norm operations, a series of aggregation operators including $$L^{q}ROF$$ L q R O F weighted averaging, $$L^{q}ROF$$ L q R O F ordered weighted averaging, $$L^{q}ROF$$ L q R O F hybrid averaging, $$L^{q}ROF$$ L q R O F weighted geometric, $$L^{q}ROF$$ L q R O F ordered weighted geometric, $$L^{q}ROF$$ L q R O F hybrid geometric operators are investigated. Some interesting aspects of these AOs are also presented. We further develop evaluation based on distance from average solution (EDAS) approach in light of the newly outlined concepts to cope with $$L^{q}ROF$$ L q R O F decision-making problems where the weight information of criteria is fully unknown, ultimately, the practicality of the framed approach is demonstrated through an empirical case, and a detailed analysis is carried out to showcase the methodology dominance.