Effectiveness validation of evaluation index systems of equipment SoS operational capability: A framework and grey clustering model

A reliable evaluation index system (EIS) is essential for assessing the operational capabilities of equipment system-of-systems (SoS), yet systematic methods for validating its effectiveness in complex scenarios remain lacking. To address this problem, this paper proposes a validation algorithm, which includes a validation framework, a data collection format tailored to operational contexts, and a grey clustering algorithm. First, the validation framework is designed at three levels, syntactic, semantic, and pragmatic, to systematically assess the normativity, logical coherence, and practical utility of the EIS. Second, a data collection format suited to operational backgrounds is introduced, enabling multi-domain coverage across the physical, informational, cognitive, and social dimensions, and accounting for both expected and abnormal scenarios. Third, a grey clustering algorithm is developed, in which a clustering weight calculation model based on the interval fuzzy preference relation matrix ensures consistency among indicators, while rough and fine clustering analyses are combined to achieve quantitative validation of EIS effectiveness. Case studies demonstrate that the proposed method effectively validates EIS performance under diverse operational conditions. Overall, this work provides a systematic basis for EIS validation and practical guidance for enhancing SoS evaluation.