The medical records in the form of images are increasing exponentially after the pandemic era. The security and copyright protection of these data are also need of the hour to protect the integrity of medical images. The proposed image watermarking method uses redundant discrete wavelet transform (RDWT), QR decomposition, and randomized singular value decomposition (RSVD) for embedding. Fuzzy inference system (FIS) is used to get the optimum scaling factor to enhance the robustness and imperceptibility. Smoothness and entropy are used as the input to FIS. To enhance the security of the proposed method hybrid watermark is generated. NIfTI (Neuroimaging informatics technology initiative) image is taken as the input host image. Aadhar card of patient is divided into two parts and then the hash values are generated by taking Aadhar number and patient number are taken as the input string to the secured hash algorithm (SHA-384, SHA-512). The average percentage improvement in imperceptibility is 5.42% and in robustness is 5.79%.