This research aims to analyze the performance of state-of-the-art machine learning techniques for classifying COVID-19 from cough sounds and to identify the model(s) that consistently perform well across different cough datasets. Different performance evaluation metrics (precision, sensitivity, specificity, AUC, accuracy, etc.) make selecting the best performance model difficult. To address this issue, in this paper, we propose an ensemble-based multi-criteria decision making (MCDM) method for selecting top performance machine learning technique(s) for COVID-19 cough classification. We use four cough datasets, namely Cambridge, Coswara, Virufy, and NoCoCoDa to verify the proposed method. At first, our proposed method uses the audio features of cough samples and then applies machine learning (ML) techniques to classify them as COVID-19 or non-COVID-19. Then, we consider a multi-criteria decision-making (MCDM) method that combines ensemble technologies (i.e., soft and hard) to select the best model. In MCDM, we use the technique for order preference by similarity to ideal solution (TOPSIS) for ranking purposes, while entropy is applied to calculate evaluation criteria weights. In addition, we apply the feature reduction process through recursive feature elimination with cross-validation under different estimators. The results of our empirical evaluations show that the proposed method outperforms the state-of-the-art models. We see that when the proposed method is used for analysis using the Extra-Trees classifier, it has achieved promising results (AUC: 0.95, Precision: 1, Recall: 0.97).