Three-way decisions are effective and heuristic methods in information processing, moreover, it provides a trisecting-and-acting framework for complex problem solving. In this paper, combining with the practical application scenario, we propose a novel three-way decisions approach and apply it to medical diagnosis. First, we build an information system which is called a hybrid information system with images by considering the characteristics of the examination items of nephritis, including urinary color, urinary tuberculosis, pH, red blood cell count, urinary irritation, computed tomography, white blood cell count and so on. Second, to describe two objects of the conditional attribute set in a hybrid information system with images, we propose the hybrid distance based on Euclidean distance. Then, the tolerance relation induced by this system is constructed. In addition, considering that missing values exist in a hybrid information system with images, interval-valued numbers are used to obtain the loss function. Given different types of parameters can respond the level of the tolerance relation and the risk preference of decision makers, and the decision rules are shown in tabular forms. Finally, an illustration is showed to verify the feasibility and reasonability of the proposed method.

三向决策是信息处理中的一种有效的启发式方法，此外，它为复杂的问题解决提供了一个三层起作用的框架。本文结合实际应用场景，提出了一种新颖的三向决策方法，并将其应用于医学诊断。首先，我们通过考虑肾炎检查项目的特征，包括尿液颜色，泌尿结核，pH，红细胞计数，尿液刺激，计算机断层扫描，白细胞，建立一个带有图像的信息系统，称为混合信息系统计数等等。其次，为了描述带有图像的混合信息系统中条件属性集的两个对象，我们提出了基于欧几里得距离的混合距离。然后，构造了由该系统引起的公差关系。另外，考虑到在具有图像的混合信息系统中存在缺失值，因此使用区间值的数字来获得损失函数。给定不同类型的参数可以响应公差关系的级别和决策者的风险偏好，并且决策规则以表格形式显示。最后，给出了一个例证来验证所提方法的可行性和合理性。