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.

中文翻译：

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具有测试成本约束的混合数据的属性尺度选择：方法和不确定性度量

最近，基于测量误差提出了几种新的成本敏感属性尺度选择方法。它们很重要，因为它们可以同时选择属性和规模组合，以最大限度地降低数据处理中消耗的成本。然而，这些方法无法处理具有测试成本约束的混合数据，并且大多没有考虑不同属性之间的尺度多样性；并且这些方法不涉及不确定度测量，所有这些都是实际应用中的重要问题。针对这种情况，本文基于粗糙集理论提出了一种有效的成本敏感属性尺度选择方法，并开发了多种相关的不确定性度量。这篇论文的主要贡献有三方面。第一的，构建了基于广义置信度向量的邻域粗糙集模型。它考虑了混合数据不同属性之间的尺度多样性。然后，开发了多种不确定性度量。它们同时考虑属性和尺度，因此比现有的仅考虑属性或仅考虑尺度的更普遍。最后，设计了一种高效的启发式属性-尺度选择算法，该算法可以选择属性及其各自的尺度，以在任意合理的测试成本上界值下最小化混合数据的消耗总成本。详细的实验彻底证实了所提出的成本敏感属性尺度选择方法的有效性。实验还揭示了不同测试成本上界对属性尺度选择和一些相关量（包括不确定性度量）的影响。本研究在一定程度上丰富了粗糙集理论，为一些测试成本受限的决策提供了有效的支持。