Hydrogen has been attracting interest as a clean and potentially sustainable energy vector for a multisectoral transition toward low-carbon emissions-based systems and economies. Recent trends in developing a hydrogen economy highlight the importance of hydrogen solid-state storage, along with production, distribution, and utilization. For purposes of storage, ongoing research efforts have considered several nanoporous materials such as carbonaceous materials, metal-organic frameworks, covalent organic frameworks, zeolites, inter-metallic hydrides, and others as promising materials. In this study, metal organic frameworks, carbonaceous materials, metal hydrides, and complex hydrides were evaluated using the fuzzy multi-criteria decision-making (FMCDM) technique to identify the optimal material in terms of surface area, capacity, dehydrogenation temperature, and stability for hydrogen storage. The method combined both quantitative and qualitative criteria in the decision structure wherein linguistic assessment under uncertainty is integrated into the decision model. A novel approach is proposed utilizing a normal distribution for the degree of indeterminacy in the linguistic scale. An illustrative case study is presented to rank the said materials for hydrogen solid-state storage. Results indicate that metal organic frameworks are the best alternative attributed to their relatively high surface area and excellent dehydrogenation temperature, while metal hydrides are the worst attributed to their relatively low surface area and sorption capacity. Sensitivity analysis was performed wherein a new approach to quantify ranking invariance and robustness is also introduced. Higher robustness values can be acquired by screening specific materials with tighter assessment virtues for selection or by narrowing down the domain of weights.