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Abstract: Although the grey model has been employed in various fields and demonstrated promising results, most applications focus on precise number predictions. However, owing to the increasing complexity of real-world problems, the grey number predictions will be more flexible and practical for grey model to describe the uncertain future tendency. For the purpose of establishing a grey model with grey number, this paper proposes a progression technique, which adopts different length series divided from the simulation data to produce a grey number prediction. Besides, this paper also modifies the algorithm of grey model, including altering the calculation of background value with an integration term and replacing the initial value of grey differential equation to the latest point, to enhance its accuracy. Two illustrative examples of numerical series and stock market are adopted for demonstrations. Results show that the proposed model can both catch the future tendency and reduce the loss of erroneous judgments. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an integration prediction method including grey model (GM), Fourier series, and Markov state transition, known as Markov–Fourier grey model (MFGM), to predict the turning time of Taiwan weighted stock index (TAIEX) for increasing the forecasting accuracy. There are two parts of forecast. The first one is to build an optimal grey model from a series of data, the other uses the Fourier series to refine the residuals produced by the mentioned model. Finally, the Markov state scheme is used for predicting the possibility of location results to promote the intermediate results generated by the Fourier grey model (FGM). It is evident that the proposed approach gets the better result performance than that of the other methods. [Copyright &y& Elsevier]

Abstract: Lowering psychological pressure of investors and increasing the futures trading profit are the main purposes of this paper. First of all, this study aims to transfer profit curve (PC) generated by a non-AI-based trading strategy into technical indices, and enable clustering of high-low points of PC to display high–low point signals through some AI-based methods such as Grey Clustering, SOM and K-mean. Next, it attempts to close the transaction with high-point signal, and then open a position at low-point one, thus constructing three groups of profit refiners: GCR (Grey Clustering Refiner), SOMR (SOM Refiner) and KMR (K-Mean Refiner). Finally, the features of these refiners are analyzed to evaluate the test results using some performance indices. SOMR could improve the profit to the greatest possible extent, followed by GCR and KMR; on the other hand, KMR could lower psychological pressure, followed by SOMR and GCR. As a whole, three groups of refiners can really improve the profit and alleviate psychological burden of investors. [Copyright &y& Elsevier]

In this paper, based on the Grey theory, a novel measurement method in a large volume and high dimension of information system is proposed for vector quantization (VQ) design and applied to image data coding. In the VQ coding procedure, it is often needs several epochs of clustering and always fails to obtain a better codebook; for instance, the well-known generalized Lloyd algorithm (GLA) easily traps into suboptimal codebook and does not have the ability to locate an optimal codebook during any clustering iteration with a random initial codebook. Hence, we propose a G2LA design to solve heavy times of clustering procedure and at least to gain the best suboptimal codebook. In order to avoid edge degradation, firstly, the new selection of initial codevectors is adopted as the fast grey vector quantization (FGVQ) procedure which chooses nonhomogeneous vectors from a large volume image data. Then extending the GLA to G2LA method by utilizing the measurement of grey relational analysis (GRA) which depends on the effect of relative objective and initial codevectors of FGVQ to obtain a better representative codebook. Experiment results show that at the same bit rate the G2LA has not only the quickly convergence time but also high quality reconstructed image than traditional GLA technique with Euclidean distance measure, especially in high dimension and a large volume data system. [Copyright &y& Elsevier]

In each training iteration of the self-organizing feature maps (SOFM), the adjustable output nodes can be determined by the neighborhood size of the winning node. However, it seems that the SOFM ignores some important information, which is the relationships that actually exist between the input training data and each adjustable output node, in the learning rule. By viewing input data and each adjustable node as a reference sequence and a comparative sequence, respectively, the grey relations between these sequences can be seen. This paper thus incorporates the grey relational coefficient into the learning rule of the SOFM, and a grey clustering method, namely the GSOFM, is proposed. From the simulation results, we can see that the best result of the proposed method applied for analysis of the iris data outperforms those of other known unsupervised neural network models. Furthermore, the proposed method can effectively solve the traveling salesman problem. [Copyright &y& Elsevier]