Different preferences of the indicators would be showed in some situations. However, the preferences are not considered into the traditional possibility functions, which are always assumed to be the linear functions. It might not be proper to analyze all kinds of indicators with the traditional possibility functions. Therefore, the universal possibility functions are provided. Due to the multiple uncertain features of the indicators, then the universal possibility functions are extended for the generalized grey numbers. According to the importance of indicators and the time, the weights of indicators and the time are given respectively. Next, generalized grey dynamic clustering models with preferences are proposed. At last, the effectiveness of the suggested methods is verified via the case illustration and comparative analysis.
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