Abstract: The traditional possibility functions are always assumed to be linear functions. The preferences of decision-makers are not considered. It might not be proper to analyze all kinds of indicators with the traditional possibility functions. Therefore, we consider the preferences and first develop the universal possibility functions. The decision-makers can obtain the appropriate universal possibility functions by adjusting the clustering preference. Then, the related properties are revealed by the proof. Next, grey clustering methods with universal possibility functions are proposed. Finally, the effectiveness of the suggested methods is verified via the case illustration and comparative analysis.

Key words: Preferences of Decision-makers, Universal Possibility Function, Clustering Preference, Grey Clustering Method