The availability of power transformers is essential for the safety and continuity of electrical service. Today's fault diagnosis methods use intelligent techniques such as neural networks, support machines, hybrid techniques, among others. Although they present good results, these techniques find restrictions in the ability to determine the precise moment in the event of multiple and small-magnitude faults. The proposal includes a new algorithm based on fuzzy rules that incorporates the daily increase of dissolved gases in the transformer oil that improves the classification of incipient faults. With reliable samples of gas dissolved in oil, the method proposed in the research can obtain a total precision rate of 91.4%. In contrast, this degree of precision is lower in other conventional methods reported in the bibliography. In addition, its performance in the classification of multiple failures is 97.5%. The method uses fuzzy logic tools to suggest actions aimed at preventive maintenance by monitoring the total of combustible gases dissolved in the oil. The proposal is a simple and easy solution to implement in practice that allows determining the status of the transformer in service without affecting the continuity of the electricity supply.