Unlocking offshore wind farms' high energy generation potential requires a comprehensive multi-disciplinary analysis that consists of intensive technical, economic, logistical, and environmental investigations. Offshore wind energy projects have high investment volumes that make it essential to execute an extensive site selection to ensure feasible investment decisions that reduce the potential financial risks. Depending on the scenario and circumstances, a ranking of alternative offshore wind energy projects helps to prioritise the investment decisions. Decision-making algorithms based on expert knowledge can support the prioritisation and thus alleviate the work load for investment decisions in the future. The case study considered here is to find the best site for a floating offshore wind farm in Norway from four pre-selected alternatives: Utsira Nord, Stadthavet, Fr⊘yabanken, Træna Vest. We propose as hybrid decision-making model a combined compromised solution (CoCoSo) based on the q-rung orthopair fuzzy sets (q-ROFSs) including the weighted q-rung orthopair fuzzy Hamacher average (Wq-ROFHA) and the weighted q-rung orthopair fuzzy Hamacher geometric mean (Wq-ROFHGM) operators. In this model, the q-ROFSs based Full Consistency Method (FUCOM) is introduced as a new methodology to determine the weights of the decision criteria. The results of the proposed model showed that the best site among the investigated four alternatives is A 1 : Utsira Nord. A sensitivity analysis verified the stability of the proposed decision-making model.