In a fuzzy multicriteria decision-making (MCDM) problem, a decision maker may have differing viewpoints on the relative priorities of criteria. However, traditional methods merge these viewpoints into a single one, which leads to an unrepresentative decision-making result. Several recent methods identify the multiple viewpoints of a decision maker by decomposing the decision maker's fuzzy judgment matrix into several symmetric fuzzy subjudgment matrices, which is an inflexible strategy. To enhance flexibility, this study proposed a fuzzy geometric mean (FGM) decomposition-based fuzzy MCDM method in which FGM is applied to decompose a fuzzy judgment matrix into several fuzzy subjudgment matrices that can be asymmetric. These fuzzy subjudgment matrices are diverse and more consistent than the original fuzzy judgment matrix. The proposed methodology was applied to select the best choice from a group of smart technology applications for supporting mobile health care during and after the COVID-19 pandemic. According to the experimental results, the proposed methodology provided a novel approach to decomposing fuzzy judgment matrices and produced more diverse fuzzy subjudgment matrices.