<p>Based on decoherence-free states and unitary operations, three multi-party semi-quantum private comparison protocols are innovatively raised to resist the collective-dephasing noise, collective-rotation noise, and collective-amplitude-damping noise, respectively. Under the crucial assistance of a semi-trustworthy third party, multiple classical participants can accurately ascertain the equality of their privacies. Notably, the classical participants execute unitary operations without the necessity to prepare new qubits, thus enhancing the qubit efficiency. Security analysis indicates that the three protocols can successfully counteract various outside and insider threats. The complex operations involved are simulated on the IBM quantum platform, respectively. Most of the existing typical protocols against collective noises are inefficient and can only resist two types of collective noise, respectively. Compared with them, the three proposed protocols not only can resist the three types of collective noises, respectively but also have higher quantum efficiency.</p>