Grey model (abbreviated as GM), which is based on Deng's grey theory, has been established as a prediction model. At present, it has been widely applied in many research fields to solve efficiently the predicted problems of uncertainty systems. However, this model has irrational problems concerning the calculation of derivative and background value z since the predicted accuracy of GM is unsatisfying when original data shows great randomness. In particular, the predicted accuracy falls in case of higher-order derivative or multivariate greatly. In this paper, the new calculation methods of derivative and background value z are first proposed to enhance the predicted power according to cubic spline function. The newly generated model is defined as 3spGM. To further improve predicted accuracy, Taylor approximation method is then applied to 3spGM model. We call the improved version as T-3spGM. Finally, the effectiveness of the proposed model is validated with three real cases.

The wavelet transform (WT) has recently emerged as a powerful tool for image compression. In this paper, a new image compression technique combining the genetic algorithm (GA) and grey-based competitive learning network (GCLN) in the wavelet transform domain is proposed. In the GCLN, the grey theory is applied to a two-layer modified competitive learning network in order to generate optimal solution for VQ. In accordance with the degree of similarity measure between training vectors and codevectors, the grey relational analysis is used to measure the relationship degree among them. The GA is used in an attempt to optimize a specified objective function related to vector quantizer design. The physical processes of competition, selection and reproduction operating in populations are adopted in combination with GCLN to produce a superior genetic grey-based competitive learning network (GGCLN) for codebook design in image compression. The experimental results show that a promising codebook can be obtained using the proposed GGCLN and GGCLN with wavelet decomposition.