Abstract: To address multi-attribute decision making problems where attribute values are interval grey numbers with partial weight information known, this study considers decision-makers’ risk preferences and integrates three-way decision theory to propose a novel grey multiattribute three-way decision model under risk preferences. Initially, in grey information systems lacking category labels and decision attributes, this model incorporates risk preferences to convert interval grey number-based evaluation values into corresponding real numbers, thereby quantifying decision information under uncertain conditions. Subsequently, grey relational analysis is employed to objectively determine conditional probabilities, significantly reducing subjective bias in decision-making. Furthermore, the model analyzes the relationship between evaluation values and loss functions, deriving a relative loss function matrix in interval grey number form, thus enhancing data reference value and improving model reliability. Building on this, this study establishes multi-attribute threeway decision rules suitable for grey environments based on risk preferences and explores the related theories of the new model. Finally, the new model is applied to the supplier selection issue, and its effectiveness, superiority, and stability are verified from multiple perspectives through comparative and experimental analysis.  

Key words: Multi-attribute decision making, Three-way decision, Interval grey number, Grey relational analysis, Relative loss function, Risk preference ,