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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]

In this paper, grey relational theory is successfully fused into the ART 1 model to construct GreyART models such as GreyARTarea and GreyARTslope. Both models possess the structure and learning ability of an ART-type NN while using grey relational analysis to process the grey information among the patterns to cluster. GreyART models could be placed in the family of ART-type NNs, the input information of which is extended from binary patterns to multi-valued patterns. Additionally, GreyART models accede to the property of ART-type NN in which the stored prototype is self-organized as a reference template during the real-time learning process. Such a property of GreyART model solves the problems in which the reference patterns have to be pre-determined in most of the grey classification methods. Computer simulations were conducted using a given pattern to examine the geometric grey-characteristic of GreyART-classifying. [Copyright &y& Elsevier]