Within the scope of the two_dimensional space with the energy and intensity of γ-ray as coordinates, we brought forward the concept of the two_dimensional fuzzy set about spectra, and established the membership function. We also introduced the fundamental principles and method for identifying the γ-ray fingerprints by fuzzy recognition technique. By regularizing the spectra, we succeeded in identifying the types and individuals of nuclear materials. Further more, we introduced the multiplying factor, and thus obtained high degree of confidence in identifying the spectra. We identified the simulation materials as radiation sources with the method, and studied the influence of the detecting distance and the detecting system fluctuation on the membership degree. The results show that the method has strong capabilities of identifying the types and the individuals of radiation sources, and can be applied to the nuclear materials safeguard.