Three-way decision based on improved aggregation method of interval loss function

Abstract Given a hybrid incomplete information table consisting both of the incomplete information table and loss function, the loss function of each object is denoted as an interval. The loss function of similarity class is defined as the aggregation of interval loss functions of all objects in its similarity class. However, existing optimistic aggregation method utilizes the union of interval loss functions of all objects in similarity class, which make the length of the aggregated interval loss function too broad. Pessimistic aggregation method utilizes the intersection of interval loss functions of all objects in similarity class, which make the length of the aggregated interval loss function too narrow. In order to get reasonable aggregated interval loss function, we propose a new aggregation method based on the principle of justifiable granularity, which make the length of the aggregated interval loss function neither too broad nor too narrow. That is, the aggregation result includes the interval loss functions of all objects in similarity class as much as possible and the aggregation result is as specific as possible. Based on the proposed aggregation method, we propose a new three-way decision model. Examples and experimental results demonstrate the effectiveness of the proposed method.

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