In this source a fuzzy approach to improve the diversity of population in genetic algorithm implementations, based on Mamdani fuzzy rules, with the tuning of crossover and mutation probabilities, is proposed. The necessary steps to implement the adaptive genetic algorithm based on fuzzy rules is outlined, in which the crossover and mutation probabilities are changed based on a Mamdani fuzzy inference system, to improve the diversity of the population of the genetic algorithm. A numerical example in real codification of chromosomes shows the effectiveness and robustness of the adaptive technique in multimodals functions. This methodology is able to modify its properties in adaptive form, and can work with complex space search, resulting in a sufficiently robust method to optimize a variety of applications. It is demonstrated from computational results that the proposed methodology presents a better performance than an ordinary genetic algorithm.