In the electric power business, power transformers are one of the most common and expensive components. The conventional diagnostic tool for understanding insulation incipient failures is the dissolved gas analysis (DGA) of transformers. Nonetheless, interpreting DGA fault gases remains a significant difficulty for engineers. Along with offline methods, a number of computational approaches have been created for DGA fault classification. Still, there exist significant hurdles in applying those methods for DGA fault classification. To establish an effective fault classification system, very diversified and massive DGA datasets of in-service transformers were collected from various utilities for this study. The dataset consists of 3147 instances with four classes: No fault, Thermal fault, low energy discharge, and high energy discharge. Models were built using various machine learning (ML) approaches like quantitative descriptive analysis (QDA), gradient boosting (GB), extra trees (ET), light GB machine (LGBM), random forest (RF), ${k}$ nearest neighbors (KNNs), naive Bayes (NB), decision tree (DT), AdaBoost (AB), logistic regression (LR), linear discriminant analysis (LDA), ridge classifier (RC), and support vector machine (SVM)-Linear Kernel. The proposed work adopts the analytic hierarchy process (AHP) technique for the estimation of weights of the criteria. Based on the generated weights, the performance of the various classifiers is assessed and ranked using multi-objective optimization based on the ratio analysis (MOORA) approach. QDA is selected as the best classifier model by the proposed technique.