Accurate evaluation of traction-elevator operational status is important for condition monitoring and maintenance decisions. However, conventional discrete classification may lose transitional information when operational indicators approach state boundaries. To address this issue, this study proposes a grey clustering evaluation method based on center-point possibility functions. A 17-indicator evaluation framework covering eight functional subsystems is established, and heterogeneous measurements are transformed into a unified dimensionless deterioration scale according to their indicator attributes. Center-point possibility functions are then constructed to characterize gradual transitions between adjacent grey classes, while CRITIC is employed to determine objective indicator weights. A grade-continuous-index dual output is further introduced to provide both categorical classification and continuous deterioration characterization. A case study of five traction elevators shows that all evaluated elevators are classified as Excellent, while the continuous status index further distinguishes their operational conditions as E2>E1>E3>E4>E5. Comparison with hard grey-class assignment demonstrates that the proposed representation retains transitional information near class boundaries and provides additional discrimination among elevators within the same dominant grey class. The proposed method provides a more informative representation of traction-elevator operational condition.