Fractal Fuzzy‑Based Multi‑criteria Assessment of Sustainability in Rare Earth Use for Hydrogen Storage

The use of rare earth elements in hydrogen storage processes offers significant advantages in terms of increasing technological efficiency and ensuring system security. However, this process also creates some serious problems in terms of environmental and economic sustainability. It is necessary to determine the most critical indicators affecting the sustainable use of these elements. Studies on this subject in the literature are quite limited, and this may lead to wrong investment decisions. The main purpose of this study is to determine the most important indicators to increase the sustainable use of rare earth elements in hydrogen storage processes. An original decision-making model in which Siamese network, logarithmic percentage-change driven objective weighting (LOPCOW), fractal fuzzy numbers, and weighted influence super matrix with precedence (WISP) approaches are integrated in the study. This study provides an original contribution to the literature by identifying the most critical indicators affecting the sustainable use of rare earths in hydrogen storage processes by presenting an innovative model. Fractal structures such as Koch Snowflake, Cantor Dust, and Sierpinski Triangle can model complex uncertainties more successfully. Fractal structures are particularly effective in modeling linguistic fuzziness because their recursive nature closely mirrors the layered and imprecise way humans often express subjective judgments. Unlike linear fuzzy sets, fractals can capture the patterns of ambiguity found in expert evaluations. Hydrogen storage capacity and government supports are determined as the most vital criteria affecting sustainability in rare earth use.