Power transformers are the most critical part of power electrical system, distribution and transmission grid. The oil and the insulation system (paper properties) degradation have many chemicals inside them, they are the result of an initial problem that can be predicted. The research has established the intelligent diagnosis system based on principal component analysis (PCA) and adaptive decision system based on fuzzy logic permits to realize a dissolved gas analysis (DGA) to predict incipient fault diagnosis by different methods, to obtain deterioration rates and health index, besides it allows to analyze the degree of polymerization (DP) for the remaining life of the equipment. The classification accuracy of the proposed method with PCA and fuzzy logic intelligent system is 97.2% for normal equipment and 98.13% for failure events. The proposed method is quite interesting for the readers and the concern researchers in the area of fuzzy mathematics and power transformers.