A (t, n) threshold private set intersection protocol allows the N participants, each holding a private set of size n, to learn the intersection of their sets only if the number of the elements in their intersection is larger than or equal to the threshold t without revealing their private information. It has a wide range of applications, such as fingerprint recognition, online carpooling, and blind date websites. However, most of the existing research on threshold protocols for private set intersections focuses on two parties. The research on the threshold protocols for multi-party private set intersections is still faced with many challenges. For example, the existing threshold protocols for multi-party private set intersections use public key algorithms with large overheads, such as the fully homomorphic encryption algorithm, and such algorithms have not yet been effectively implemented. To solve the above problems, this study combines robust secret sharing and Bloom filters to propose two effective multi-party threshold private set intersection protocols and implements the protocols by simulation for the first time. Specifically, this study designs a new construction method for Bloom filters. The shares generated by robust secret sharing are corresponded to the elements in the sets of the participants. Whether the number of the elements in the intersection of the parties reaches the threshold is determined by whether correct secrets can be reconstructed from the secret sub-shares obtained by querying the Bloom filter. In this way, the protocols effectively prevent the revealing of the intersection cardinality. The first protocol designed in this study avoids public key algorithms with large overheads. When the security parameter λ is set to 128, the set size n is set to 2¹⁴ and the threshold is set to 0.8n, the time cost of the online phase of the protocols in the three-party scenario is 191 s. In addition, to resist the collusion of at most N – 1 adversaries in the semi-honest model, this study combines oblivious transfer with the first protocol to design a variant of the first protocol. Under the same condition, the time cost of the online phase is 194 s. Finally, the security proof conducted proves that the proposed protocols are secure in the semi-honest model.