Abstract: Intuitionistic fuzzy decision systems are generalizations of fuzzy decision systems, where condition attribute values are intuitionistic fuzzy elements. The objective of this paper is the intuitionistic fuzzy ordered decision system, in which the attributes are preference-ordered. First, the concept of partially consistent reduct is introduced in intuitionistic fuzzy ordered decision systems. And it is proven that in consistent intuitionistic fuzzy ordered decision systems, the partially consistent reducts and relative reducts are the same, which suggests that the partially consistent reduct is indeed a meaningful extension of relative reduct for inconsistent intuitionistic fuzzy ordered decision systems. Second, the partially consistent discernibility matrix as well as the partially consistent discernibility function is given to compute all the partially consistent reducts of intuitionistic fuzzy ordered decision systems. Then, two equivalent definitions of the partially consistent reduct, the lower reduct and lower approximation reduct, are proposed to demonstrate its validity from other viewpoints. Finally, a numerical example is employed to illustrate the conceptual arguments throughout the present paper.

Key words: intuitionistic fuzzy ordered decision system, dominance-based rough set, partially consistent reduct, discernibility matrix

摘要： 直觉模糊决策系统是模糊决策系统的扩展，其中条件属性值均为直觉模糊元。讨论属性值之间带有序关系的直觉模糊决策系统，即直觉模糊序决策系统。首先，引入直觉模糊序决策系统的部分一致约简，并证明了在一致直觉模糊序决策系统中，部分一致约简恰为相对约简，因此部分一致约简是相对约简在不一致直觉模糊序决策系统中的扩展。其次，给出求解直觉模糊序决策系统全部部分一致约简的部分一致辨识矩阵和辨识函数。然后，介绍了部分一致约简的两种等价形式：下约简和下近似约简。最后，用实例验证了约简计算方法的可行性。

关键词: 直觉模糊序决策系统, 优势粗糙集, 部分一致约简, 辨识矩阵