Abstract: This paper supposes the given data follow two-dimension uniform distribution. Interval-valued information system has been investigated based on dominance relationship. Probabilistic rough set model based on [α]dominance relationship has been established by defining [Paji] which shows the probability of attribute object[xj]superior to object[xi], together with relative entropy optimality criteria. Meanwhile, decision also can be made through [α]cumulative probability even appearance of the indistinguishable situation. The model has been applied to a practical example of interval number group decision-making about radar countermeasures targets, and the result has suggested that in appropriate granularity, different decision-maker can make interval number group decision according to different preference with the above model, and flexibly choose dominance relationship in appropriate granularity, and the model has been demonstrated its feasibility and effectiveness.

Key words: dominance relationship, uniform distribution, relative entropy, rough set, granularity

摘要： 讨论优势关系下的区间值信息系统在二维均匀分布的假设条件下，通过定义属性对象[xj]优于[xi]的概率[Paji]，结合相对熵最优准则，建立[α]-优势关系的概率粗糙模型，探讨了即使出现不可分辨情况，也可通过[α]-累积概率加以决策。模型应用于雷达作战目标的区间数群决策实例分析中，结果显示：[α]-优势关系的概率粗糙模型可根据不同的决策者，不同的偏好，在合适的粒度，灵活选择粗细适当的优势关系，进行区间数群决策，模型可行有效。

关键词: 优势关系, 均匀分布, 相对熵, 粗糙集, 粒度