Hypergraph　representation　learning　(HGRL)　has　attracted　widespread　attention　for　its　ability　to　capture　high-order　relationships　(simultaneous　interactions　among　multiple　entities)　in　hypergraphs.　However,　most　existing　HGRL　methods　struggle　with　uncertainties　throughout　HGRL　processes,　including　input　signals,　message　passing,　and　inference.　These　uncertainties,　such　as　redundant　or　noisy　attributes,　distorted　structures,　noisy　node/hyperedge　representations,　and　parameter　estimation　biases,　undermine　model　robustness　and　reliability.　To　address　this　issue,　we　introduce　fuzzy　logic　into　HGRL　for　the　first　time,　and　propose　a　new　HGRL　framework　called　fuzzy　hypergraph　representation　learning　and　inference　(FHRLI).　It　effectively　manages　uncertainties　from　both　data　and　model　perspectives,　resulting　in　more　expressive　representations.　In　addition,　it　allows　for　more　precise　and　robust　inference　based　on　uncertain　evidence.　Contemplating　the　influence　of　label　scarcity　and　uncertainties　(annotation　errors),　we　further　develop　an　unsupervised　HGRL　algorithm,　named　fuzzy　hypergraph　contrastive　representation　learning　(FHCRL),　by　combining　the　proposed　FHRLI　framework　with　hypergraph　contrastive　learning.　Extensive　experiments　across　various　tasks　verify　the　effectiveness　and　competitiveness　of　the　proposed　FHRLI　framework　and　FHCRL　compared　to　the　state-of-the-art　baselines.　Furthermore,　we　experimentally　demonstrate　that　the　proposed　FHRLI　framework　can　achieve　superior　robustness　and　wide　universality,　along　with　providing　a　certain　explanatory　analysis.　©　1993-2012　IEEE.