Recently several novel cost-sensitive attribute-scale selection approaches have been proposed based on measurement errors. They are significant because they can simultaneously select attributes and scale combination to minimize the cost consumed in data processing. However, these approaches cannot deal with hybrid data with test cost constraint, and most of them do not consider the scale diversity between different attributes; and these approaches do not touch the uncertainty measurement, all of which are important issues in real applications. To address this situation, in this paper an effective cost-sensitive attribute-scale selection approach is presented based on the rough set theory, and multiple relevant uncertainty measures are developed. The main contributions of the paper are threefold. First, a generalized confidence level vector-based neighborhood rough set model is constructed. It takes into account the scale diversity between different attributes of hybrid data. Then, multiple uncertainty measures are developed. They consider both attributes and scales, thus are more general than existing ones which consider only attributes or only scales. Finally, an efficient heuristic attribute-scale selection algorithm is designed, which can select attributes and their respective scales to minimize the consumed total cost of hybrid data under any rational value of test cost upper bound. Detailed experiments thoroughly confirm the effectiveness of the proposed cost-sensitive attribute-scale selection approach. The experiments also reveal the influences of different test cost upper bounds to the attribute-scale selection and some related quantities including the uncertainty measures. This study would enrich the rough set theory to some extent, and provide an effective support for some test cost-constrained decision makings.