The existing attribute reduction algorithms mostly focus on all decision classes in decision systems, but in actual decision process, decision makers may only focus on one or several decision classes in the decision systems. To solve this problem, a theoretical framework of positive region preservation reduction based on multi-specific decision classes in incomplete decision systems was proposed. Firstly, the positive region preservation reduction for single specific decision class in incomplete decision systems was defined. Secondly, the positive region preservation reduction for single specific decision class was extended to multi-specific decision classes, and the corresponding discernibility matrix and function were constructed. Thirdly, with related theorems analyzed and proved, an algorithm of Positive region preservation Reduction for Multi-specific decision classes reduction based on Discernibility Matrix in incomplete decision systems (PRMDM) was proposed. Finally, four UCI datasets were selected for experiments. On Teaching-assistant-evaluation, House, Connectionist-bench and Cardiotocography dataset, the average reduction length of Positive region preservation Reduction based on Discernibility Matrix in incomplete decision systems (PRDM) algorithm is 4.00, 13.00, 9.00 and 20.00 respectively while that of the PRMDM algorithm (with decision classes in the multi-specific decision classes is 2) is 3.00, 8.00, 8.00 and 18.00 respectively. The validity of PRMDM algorithm is verified by experimental results.