This study proposes an automatic genetic algorithm in fuzzy cluster analysis for numerical data. In this algorithm, a new measure called the FB index is used as the objective function of the genetic algorithm. In addition, the algorithm not only determines the appropriate number of groups but also improves the steps of traditional genetic algorithm as crossover, mutation and selection operators. The proposed algorithm is shown the step by step throughout the numerical example, and can perform fast by the established Matlab procedure. The result from experiments show the superiority of the proposed algorithm when it overcomes the existing algorithms. Moreover, it has been applied in recognizing the image data, and building the fuzzy time series model. These show the potential of this study for many real applications of the different fields.