Abstract: The decision system can be divided into coordinated decision system and uncoordinated decision system. Generally, the reductions of these two kinds of systems are inconsistent. This paper first introduces the basic concepts of relative reduction, relative belief reduction and relative plausibility reduction, and then sufficient unnecessary conditions of intuitionistic fuzzy rough sets with numerical characteristics are given. It is proven that the upper and lower approximation operators are additive and multiplicative. Then, the consistency of the decision system is analyzed. It turns out that relative reduction, relative belief reduction and relative plausibility reduction are equivalent when the decision system is consistent; when the decision system is inconsistent, the reduction of the inconsistent decision system is equivalent to the consistent decision system under the generalized decision advan-tage relationship. Based on the analysis, the research on the reduction of the intuitionistic fuzzy rough set decision system is further perfected.

Key words: intuitionistic fuzzy, evidence theory, knowledge reduction, decision system

摘要： 决策系统可划分为协调决策系统和不协调决策系统，两种系统的约简通常不一致。首先介绍相对约简、相对信任约简和相对似然约简的基本概念，并给出直觉模糊粗糙集具有数值特征的充分不必要条件，即上、下近似算子具有可加性和可乘性。然后分析决策系统的一致性，当为协调决策系统时，直觉模糊决策系统的相对约简、相对信任约简和相对似然约简三者等价；当为不协调决策系统时，在广义决策优势关系下，不协调决策系统的约简与协调决策系统等价。通过上述研究，进一步完善了直觉模糊粗糙集决策系统约简的研究。

关键词: 直觉模糊, 证据理论, 知识约简, 决策系统