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

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