<p>Binocular rivalry is a cyclic process involving perceptual choice and dominance duration, commonly intertwined with attention and noise. Recent work primarily emphasized potential functional role of noise during perceptual dominance duration stage, while overlooking its impact on perceptual choice. Here, the attention model of binocular rivalry subjected to multiplicative and additive noises was investigated. The numerical results revealed that the noise plays a crucial role in the perceptual choice. (i) Formation of perceptual choice was accompanied by differences in binocular relaxation time, with the relaxation time of dominant perception being longer than that of non-dominant perception. In addition, there exists a correlation between mean perceptual choice time and relaxation time. (ii) The observation of coherence resonance induced by the additive noise indicates that binocular perceptions can achieve the most stable perceptual choice. (iii) The attention bias caused by binocular fluctuation difference can lead to perceptual choice preference, with the most significant perceptual choice preference being associated with occurrence of the resonance excitation and suppression. These findings have the important implication for a deeper understanding of binocular rivalry and decision-making.</p>