Graph　representation　learning　focuses　on　abstracting　critical　information　from　raw　graphs.　Unfortunately,　there　always　exist　various　kinds　of　uncertainties,　such　as　attribute　noise　and　network　topology　corruption,　in　raw　graphs.　Under　the　message　passing　mechanism,　certainties　are　likely　to　spread　throughout　the　whole　graph.　Matters　like　these　would　induce　deep　graph　models　into　producing　uncertain　representations　and　restrict　representation　expressiveness.　Considering　this,　we　propose　a　pioneering　framework　to　defend　graph　uncertainties　by　improving　the　robustness　and　capability　of　graph　neural　networks　(GNNs).　In　our　framework,　we　consider　that　weights　and　biases　are　all　fuzzy　numbers,　thus　generating　representations　to　assimilate　graph　uncertainties,　which　are　finally　released　by　defuzzification.　To　describe　the　process　of　the　framework,　in　this　article,　a　graph　convolutional　network　(GCN)　is　employed　to　construct　a　robust　graph　model,　called　FuzzyGCN.　To　verify　the　effectiveness　of　FuzzyGCN,　it　is　trained　in　both　supervised　and　unsupervised　ways.　In　the　supervised　setting,　we　find　that　FuzzyGCN　has　stronger　power　and　is　more　immune　to　data　uncertainties　when　compared　with　various　classical　and　robust　GNNs.　In　the　unsupervised　setting,　FuzzyGCN　surpasses　many　state-of-the-art　models　in　node　classification　and　community　detection　over　several　real-world　datasets.