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中文摘要：
传统粗糙集理论是基于等价关系来对信息系统进行属性约简的。对于带有决策属性的信息系统，当决策属性值为直觉模糊数的时候，不能直接用粗糙集理论进行属性约简。该文在直觉模糊决策信息系统中引入优势关系。基于优势关系，定义了条件属性集的下近似决策协调集，建立了条件属性集的下近似约简模型，同时给出下近似约简的判定定理以及算法步骤。在一些决策属性值为直觉模糊数的决策信息系统中，利用该文提出的下近似约简方法，可以得到更为简洁的决策规则。最后给出一个实例验证算法的有效性。
英文摘要：
The traditional rough set theory performs attributes reduction for information systems based on equivalence relation. But we cannot use the traditional rough set theory directly to reduce the attributes of Intuitionistic Fuzzy decision Information Systems （IFDIS）, because decision attribute values in IFDIS are intuitionistic fuzzy numbers. In this paper, we introduce the dominance relation to IFDIS. Based on dominance relation, we give a new definition for lower approximation decision consistent set of the condition attribute sets. The lower approximation reduction model of the condition attribute sets is established. The algorithm to compute the lower approximation reduction and the judgment theorem of lower approximation reduction are also given. In some decision information systems which decision attribute values are intuitionistic fuzzy numbers, we can get more concise decision rules via the lower approximation reduction method proposed in this paper. Finally, an example is given to illustrate the effectiveness of our algorithm.
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