The decarbonization of electric power systems plays a critical role in global endeavors to mitigate climate change and facilitate the transition towards a sustainable energy future. In this context, green hydrogen has emerged as a promising and nascent clean energy solution, showing substantial potential for addressing the prevailing energy and environmental challenges on a global scale. This paper proposes an integrated energy hub (IEH) operational model to produce green hydrogen from biomass. This model includes renewable photovoltaic and wind sources, biomass electrolyzers, batteries, and hydrogen storage systems (HSS). To effectively manage the uncertainties stemming from renewable sources, electricity and hydrogen demand, and energy prices, an Information Gap Decision Theory-based normalized weighted-sum (IGDT-NWS) approach is proposed. For the first time, this approach solves multi-objective problems with operation costs, carbon emissions, and the energy export index while accounting for uncertainties to mitigate adverse impacts. The planning obtained for IEH with a risk-averse strategy, where the critical deviation factor is 0.1, is robust against the maximum prediction error of electricity demand, hydrogen demand, the output of PV and WT, and the electricity price of 5 %, 1.24 %, 10 %, 7.06 %, and 17.2 %, respectively. With a risk-seeker strategy, our proposed method can optimistically reduce operation cost by 10 % with the deviation of 4.83 %, 5.86 %, 10 %, 0 %, and 5 %, respectively. Moreover, this study emphasizes the potential benefits of integrating HSS into the battery energy storage system (BESS). The results show that the proposed model decreases IEH operation cost by 35.29 %, reduces environmental impact by 33.37 %, and improves EEI by 71.6 %, compared with using BESS only.