Criteria weights are essential in various multi-criteria decision-making (MCDM) approaches. The amount of weight indicates the criterion's importance, and the performance of MCDM techniques depends on the correct estimation of criteria weights and criteria amount in the decision matrix. The distance correlation-based CRiteria Importance Through Inter-criteria Correlation (CRITIC) technique is a modified version of the CRITIC method. Since Pearson's correlation is sensitive to noisy and outlier data, this paper proposes using the biweight midcorrelation as a robust alternative to Pearson's correlation. The weights obtained from the proposed biweight midcorrelation method make using the full range of MCDM techniques possible. This study examined the performance of the proposed method in comparison with eight criteria weighting techniques on the electric supply for a Building-Integrated PhotoVoltaic (BIPV) problem. Results from three different tests (i.e. distance correlation, Spearman rank-order correlation, and symmetric mean absolute percentage error (sMAPE)) indicated that the proposed method could produce more valid criteria weights and ranks than other methods. The value of the sMAPE criterion for the proposed method is 0.1096. Sensitivity analysis also revealed that the proposed method provides more robust criteria weights and ranks with a larger decision matrix.