In this paper, we propose a new wavelet shrinkage algorithm based on fuzzy logic. In particular, intra-scale dependency within wavelet coefficients is modeled using a fuzzy feature. This feature space distinguishes between important coefficients, which belong to image discontinuity and noisy coefficients. We use this fuzzy feature for enhancing wavelet coefficients' information in the shrinkage step. Then a fuzzy membership function shrinks wavelet coefficients based on the fuzzy feature. In addition, we extend our noise reduction algorithm for multi-channel images. We use inter-relation between different channels as a fuzzy feature for improving the denoising performance compared to denoising each channel, separately. We examine our image denoising algorithm in the dual-tree discrete wavelet transform, which is the new shiftable and modified version of discrete wavelet transform. Extensive comparisons with the state-of-the-art image denoising algorithm indicate that our image denoising algorithm has a better performance in noise suppression and edge preservation.