Uncertainty-aware type-II fuzzy graph modeling of resting-state fMRI uncovers robust sex differences.

BACKGROUND: Resting-state fMRI connectivity is commonly estimated by single-value correlations that ignore run-to-run variability and sampling uncertainty, potentially obscuring subtle group effects such as sex-related differences in network stability. NEW METHOD: We introduce a novel interval Type-II fuzzy graph framework that encodes connectivity uncertainty via block-bootstrap bounds across four HCP resting-state runs and derives stable α-cut graphs. We quantify uncertainty-aware stability using Disintegration Index (DI), Span Integrity (SI), and their composite DI×SI at both global and node-wise levels. RESULTS: Sex differences in DI×SI were robust but depended on the parcellation scheme. Using a macro-anatomical Standard atlas (cortex + subcortex), females showed higher composite stability in the conservative-to-intermediate α regime, consistent with a more stable high-certainty cortico-subcortical backbone. In contrast, using the cortical Yeo17 functional-network atlas, males showed higher DI×SI across comparable α ranges, indicating relatively greater stability of intra-cortical functional-network organization. Node-wise effects likewise differed across atlases, highlighting subcortical hubs in the Standard representation and distributed cortical networks in Yeo17. These effects were most pronounced in the conservative low-to-intermediate α regime. COMPARISON WITH EXISTING METHODS: A matched crisp Pearson-correlation baseline yielded substantially smaller and less stable effect sizes, showing that uncertainty-aware modeling increases sensitivity to reproducible and cross-run stable sex effects. CONCLUSIONS: Type-II fuzzy connectomics reveals robust, α-dependent sex differences whose direction depends on atlas level, providing complementary insights into whole-brain versus cortical-network stability.