Due to its quantitative capacity to differentiate Fermatean fuzzy sets (FFSs),
distance measurement is a research hotspot in the Fermatean fuzzy set. For Fermatean
fuzzy sets, we used cosine distance, a novel distance metric. In this study, measures of
cosine similarity and cosine distance amongst FFSs are taken into account when trying
to solve a multi-attribute decision-making problem based on sustainable development
goals. In this study, we used the cosine distance measure for Fermatean fuzzy set
theory to rank a set of urban cities according to many factors, including poverty, health,
industrial development, and climate quality. Additionally, a suitable example is used to
illustrate the superiority and logic of the present formulation.
Keywords: Cosine distance, Cosine similarity, Fermatean fuzzy sets, Multiattribute decision making, Sustainable Development Goals.