In 2020, Ashraf et al. proposed an interval type-2 fuzzy logic based block similarity calculation using color proximity relations of neighboring pixels in a steganographic scheme. Their method works well for detecting similarity, but it has drawbacks in terms of visual quality, imperceptibility, security, and robustness. Using Mamdani fuzzy logic to identify color proximity at the block level, as well as a shared secret key and post-processing system, this paper attempts to develop a robust data hiding scheme with similarity measure to ensure good visual quality, robustness, imperceptibility, and enhance the security. Further, the block color proximity is graded using an interval threshold. Accordingly, data embedding is processed in the sequence generated by the shared secret keys. In order to increase the quality and accuracy of the recovered secret message, the tampering coincidence problem is solved through a post-processing approach. The experimental analysis, steganalysis and comparisons clearly illustrate the effectiveness of the proposed scheme in terms of visual quality, structural similarity, recoverability and robustness.