By examining the memory effect and the fuzziness of human subjective judgment, the fuzzy relation between physical meaningless random noise stimuli and the psychological response is clarified quantitatively based on bivariate membership functions. Two variables describing the sound pressure level of the random noise stimulus and the temporal change in the level are employed as the fundamental variables for the bivariate membership functions. A method for predicting the psychological response to such stimuli is proposed, introducing the concept of fuzzy probability. The validity and usefulness of the proposed method is confirmed experimentally by applying the method to observed data. The theoretical calculations are in good agreement with the experimental results.