Many power transformers throughout the world are nearing or have gone beyond their theoretical design life. Since these important assets represent approximately 60% of the cost of the substation, monitoring their condition is necessary. Condition monitoring helps in the decision to perform timely maintenance, to replace equipment or extend its life after evaluating if it is degraded. The challenge is to prolong its residual life as much as possible. Dissolved Gas Analysis (DGA) is a well-established strategy to warn of fault onset and to monitor the transformer’s status. This paper proposes a new intelligent system based on DGA; the aim being, on the one hand, to overcome the conventional method weaknesses; and, on the other hand, to improve the transformer diagnosis efficiency by using a four-step powerful artificial intelligence method. (1) Six descriptor sets were built and then improved by the proposed feature reduction approach. Indeed, these six sets are combined and presented to a Kohonen map (KSOM), to cluster the similar descriptors. An averaging process was then applied to the grouped data, to reduce feature dimensionality and to preserve the complete information. (2) For the first time, four direct Multiclass Support Vector Machines (M-SVM) were introduced on the Generic Model basis; each one received the KSOM outputs. (3) Dempster–Shafer fusion was applied to the nine membership probabilities returned by the four M-SVM, to improve the accuracy and to support decision making. (4) An output post-processing approach was suggested to overcome the contradictory evidence problem. The achieved AUROC and sensitivity average percentages of 98.78–95.19% (p-value < 0.001), respectively, highlight the remarkable proposed system performance, bringing a new insight to DGA analysis.