This study presents the implementation of Multi-Criteria Decision-Making (MCDM) methodologies, particularly the fuzzy technique for order of preference by similarity to ideal solution (TOPSIS), in prioritizing technosignatures (TSs) for the search for extraterrestrial intelligence (SETI). By incorporating expert opinions and weighted criteria based on the established Axes of Merit, our analysis offers insights into the relative importance of various TSs. Notably, radio and optical communications are emphasized, in contrast to dark side illumination and starshades in transit. We introduce a new axis, Scale Sensitivity, designed to assess the variability of TS metrics. A sensitivity analysis confirms the robustness of our approach. Our findings, especially the highlighted significance of artifacts orbiting Earth, the Moon, or the Sun, indicate a need to broaden evaluative criteria within SETI research. This suggests an enhancement of the Axes of Merit, with a focus on addressing the plausibility of TSs. As the quest to resolve the profound question of our solitude in the cosmos continues, SETI efforts would benefit from exploring innovative prioritization methodologies that effectively quantify TS search strategies.