In data assimilation for numerical weather prediction, observation errors are typically neglected or are assumed to have zero correlations, resulting in a loss of information. For spurious correlations in data assimilations of limited ensemble sizes, a new method is proposed by calculating observation distances and constructing equivalent observation position weights. Coupled with standard fuzzy control algorithms, a fuzzy control ensemble transform Kalman filter (FETKF) is presented, and the corresponding procedures are given. Within the framework of the classical Lorenz-96 chaotic model, we compare the performance of the ensemble transform Kalman filter (ETKF), the local ensemble transform Kalman filter (LETKF), and the proposed FETKF with varying physical parameters. Comparisons are drawn between the LETKF localization coefficients and FETKF spatial distance vectors to calculate the corresponding weight function of the chaotic model. The results show that the new method can eliminate spurious correlations, prevent long-range observation effects of state update variables and reduce analysis errors. The error handling methods based on fuzzy control performed well under both perfect and imperfect model scenarios in the Lorenz-96 model.