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Cities are the main sites of production, employment, and capital accumulation in advanced economies, which places urban economic performance at the centre of economic policy and urban governance. This work develops an integrated grey-based multi-criteria approach for assessing that performance and applies it to the sixteen G7 cities covered by the Global Power City Index (GPCI). Criterion weights are obtained with Grey RANCOM (G-RANCOM), which converts the ordinal rankings of a five-member expert panel into interval weights, and the cities are ranked with Grey MUNRA (G-MUNRA), which aggregates linear, vector, and non-linear normalization. Each performance entry is an interval bounded by the minimum and the maximum annual score observed in the GPCI Economy function over 2021–2025. Market size, economic vitality, and business environment emerge as the most influential criteria, and New York, London, and Tokyo occupy the highest positions, while Osaka, Milan, and Fukuoka occupy the last three. Robustness is tested via scenario analyses on the model parameters and through a global analysis of 100,000 replications in which all of them vary jointly. New York holds the first position in 74% of the replications and the three lowest positions are unchanged in 87%, whereas cities in adjacent middle positions are not separated reliably. Rankings produced by five established grey approaches, by crisp and fuzzy counterparts, and by the published GPCI Economy rankings agree with the reported ordering, with Spearman correlations between 0.92 and 1.00. The framework offers urban policymakers a transparent benchmarking tool for evidence-based competitiveness strategies. Full article