This article proposes the genetic algorithm in fuzzy clustering problem for interval value (IGI). In this algorithm, we use the overlap divergence to assess the similarity of the intervals, and take the new index (IDB) as the objective function to build the IGI. The crossover and selection operators in IGI are modified to optimize the results in clustering. The IGI not only determines the suitable number of groups, optimizes the result of clustering but also finds the probability of assigning the elements to the established clusters. The proposed algorithm is also applied in image recognition. The convergence of the IGI is considered and illustrated by the numerical examples. The complex computations of the IGI are performed conveniently and efficiently by the built Matlab program. The experiments on the data-sets having different characteristics and elements show the reasonableness of the IGI, and its advantages overcome other algorithms.