<p>Multi-scale decision systems present data in multiple granularities at different scale levels, which is conducive to the multilevel knowledge representation and discovery of specific complex data in reality. However, the existing multi-scale decision systems have difficulties in handling mixed-attribute data with both numerical and nominal attributes. To address the optimal scale selection for mixed-attribute data in the multi-scale decision system, a similarity relation based on adjusted cosine similarity and inverted specific-class distance metric is put forward, which transforms the ordered numerical attributes into attribute vectors and processes them with adjusted cosine similarity, and handles the unordered nominal attributes with the inverted specific-class distance metric. A multi-scale decision system is transformed into a multi-scale covering decision system by forming a covering over the universe of discourse through the proposed similarity relation. Subsequently, in the transformed multi-scale covering decision system, an optimal scale selection method based on covering rough entropy is presented to obtain the optimal scale satisfying the demand. The experimental results on the UCI datasets show that by using the proposed similarity relation to divide the universe of discourse of mixed-attribute data into similarity classes, it can significantly reduce the number of divisions in the universe of discourse while still maintaining a relatively high approximate classification accuracy and approximate classification quality. Moreover, the proposed optimal scale selection method for multi-scale decision system exhibits excellent performance in handling datasets with both numerical and nominal attributes.</p>