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The decomposition of sounds into sines, transients, and noise is a long-standing research problem in audio processing. The current solutions for this three-way separation detect either horizontal and vertical structures or anisotropy and orientations in the spectrogram to identify the properties of each spectral bin and classify it as sinusoidal, transient, or noise. This paper proposes an enhanced three-way decomposition method based on fuzzy logic, enabling soft masking while preserving the perfect reconstruction property. The proposed method allows each spectral bin to simultaneously belong to two classes, sine and noise or transient and noise. Results of a subjective listening test against three other techniques are reported, showing that the proposed decomposition yields a better or comparable quality. The main improvement appears in transient separation, which enjoys little or no loss of energy or leakage from the other components and performs well for test signals presenting strong transients. The audio quality of the separation is shown to depend on the complexity of the input signal for all tested methods. The proposed method helps improve the quality of various audio processing applications. A successful implementation over a state-of-the-art time-scale modification method is reported as an example.