The lack of object-level labels presents a significant challenge for 3D object retrieval in the open-set environment. However, part-level shapes of objects often share commonalities across categories but remain underexploited in existing retrieval methods. In this paper, we introduce the Hypergraph-Based Assembly Fuzzy Representation (HARF) framework, which navigates the intricacies of open-set 3D object retrieval through a bottom-up lens of Part Assembly. To tackle the challenge of assembly isomorphism and unification, we propose the Hypergraph Isomorphism Convolution (HIConv) for smoothing and adopt the Isomorphic Assembly Embedding (IAE) module to generate assembly embeddings with geometric-semantic consistency. To address the challenge of open-set category generalization, our method employs high-order correlations and fuzzy representation to mitigate distribution skew through the Structure Fuzzy Reconstruction (SFR) module, by constructing a leveraged hypergraph based on local certainty and global uncertainty correlations. We construct three open-set retrieval datasets for 3D objects with part-level annotations: OP-SHNP, OP-INTRA, and OP-COSEG. Extensive experiments and ablation studies on these three benchmarks show our method outperforms current state-of-the-art methods.