Abstract: The generalized decision distribution function of objective random information system is given. The μ-reduction based on objects in inconsistent objective random information systems under the equivalent relation and dominance- equivalent relation are proposed. Meanwhile some properties, the judgment theorem and calculation approach of μ-reduction are obtained. Finally, a numerical example is used to illustrate the validity of this calculation method.

Key words: inconsistent objective random information system, equivalent relation, dominance-equivalent relation, μ-reduction

摘要： 给出目标随机信息系统的广义决策分布函数，分别引入等价关系和优势-等价关系下的两种不协调目标随机信息系统中基于对象的μ-约简的概念，得到了μ-约简的一些性质和μ-约简的判定方法及计算方法，最后用实例验证了μ-约简计算方法的有效性。

关键词: 不协调目标随机信息系统, 等价关系, 优势-等价关系, &mu, -约简