The fuzzy possibilistic c-means (FPCM) is embedded into a 2-D Hopfield neural network termed the fuzzy possibilistic Hopfield network (FPHN) to generate an optimal solution for vector quantization (VQ) in the discrete cosine transform (DCT) and the Hadamard transform (HT) domains. The information transformed by DCT or HT is separated into dc and ac coefficients. Then, the ac coefficients are trained using the proposed methods to generate a better codebook based on VQ. The energy function of the FPHN is defined as the fuzzy membership grades and possibilistic typicality degrees between training samples and codevectors. A near global-minimum codebook in the frequency domains can be obtained when the energy function converges to a stable state. Instead of one state in a neuron for the conventional Hopfield nets, each neuron occupies two states called the membership state and the typicality state in the proposed FPHN. The simulated results show that a valid and promising codebook can be generated in the DCT or HT domains using the FPHN.