Basic particle swarm optimization(PSO) algorithm only depends on individual and social cognition, but the
cognitive part of PSO is uncertain for random behavior of cognitive factors. Therefore, uncertain knowledge is introduced to the basic PSO to improve the knowledge structure of each particle. Random cognitive factors normalization is also considered in the PSO-UK algorithm to ensure complete knowledge for the PSO-UK algorithm. Theoretical analysis and simulations show that the PSO-UK algorithm has the performance of global convergence and better precision value of local convergence than the basic PSO.