The cross-sections of the 127I (n, 2n) 126I and 133Cs (n, 2n) 132Cs reactions at the 13.83 ± 0.2, 14.33 ± 0.2 and 14.79 ± 0.2 MeV neutron energies were measured relative to the 93Nb (n, 2n) 92mNb reaction through the activation technique in combination with off-line γ-ray spectrometry. The neutron beam was generated from the T (d, n) 4He reaction using the K-400 neutron generator at the Chinese Academy of Engineering Physics (CAEP). Considering the correlations between different attributes, detailed uncertainty propagation was performed using the covariance analysis, and the cross-sections were reported with their uncertainties and correlation matrix. The uncertainty of the measurement cross-sections ranges from 4.84 to 5.90%, which is lower than the previous experimental data. Furthermore, the theoretical excitation function of 127I (n, 2n) 126I and 133Cs (n, 2n) 132Cs reactions were calculated using the TALYS-1.95 and EMPIRE-3.2.3 codes. Then, experimentally determined cross-sections were analyzed by comparing with the literature data available in the EXFOR database and evaluated nuclear data of the ENDF/B-VIII.0, JEFF-3.3, JENDL-5, BROND-3.1, CENDL-3.2, and TENDL-2019 databases. Compared with the values prior reported in the 13.8-14.8 MeV energies region, the precision of the results obtained in this work is greatly improved. The current experimental results with thorough uncertainties and covariance information are critical for verifying the reliability of the theoretical model and improving the quality of the nuclear database.