At present, the scale of interval type data is getting larger and larger. When using the classic attribute reduction method to process, the data needs to be preprocessed,thus leading to the loss of original information. To solve this problem, a β-distribution reduction algorithm of the interval-valued decision system was proposed. Firstly, the concept and the reduction target of β-distribution of the interval-valued decision system were given, and the proposed related theories were proved. Then, the discernibility matrix and discernibility function of β-distribution reduction were constructed for the above reduction target,and the β-distribution reduction algorithm of the interval-valued decision system was proposed. Finally,14 UCI datasets were selected for experimental verification. On Statlog dataset, when the similarity threshold is 0.6 and the number of objects is 100, 200, 400, 600 and 846 respectively, the average reduction length of the β-distribution reduction algorithm is 1.6, 2.2, 1.4, 2.4 and 2.6 respectively, the average reduction length of the Distribution Reduction Algorithm based on Discernibility Matrix(DRADM) is 2.0, 3.0, 3.0, 4.0 and 4.0 respectively, the average reduction length of the Maximum Distribution Reduction Algorithm based on Discernibility Matrix(MDRADM) is 2.0, 3.0, 3.0, 4.0 and 3.0 respectively. The effectiveness of the proposed β-distribution reduction algorithm is verified by experimental results.

There are a large number of dynamically-increasing interval data in practical applications. If the classic non-incremental attribute reduction of positive region is used for reduction, it is necessary to recalculate the positive region reduction of the updated interval-valued datasets, which greatly reduces the computational efficiency of attribute reduction. In order to solve the problem, incremental attribute reduction methods of positive region in interval-valued decision tables were proposed. Firstly, the related concepts of positive region reduction in interval-valued decision tables were defined. Then, the single and group incremental mechanisms of positive region were discussed and proved, and the single and group incremental attribute reduction algorithms of positive region in interval-valued decision tables were proposed. Finally, 8 UCI datasets were used to carry out experiments. When the incremental size of 8 datasets increases from 60% to 100%, the reduction time of classic non-incremental attribute reduction algorithm in the 8 datasets is 36.59 s, 72.35 s, 69.83 s, 154.29 s, 80.66 s, 1498.11 s, 4124.14 s and 809.65 s, the reduction time of single incremental attribute reduction algorithm is 19.05 s, 46.54 s, 26.98 s, 26.12 s, 34.02 s, 1270.87 s, 1598.78 s and 408.65 s, the reduction time of group incremental attribute reduction algorithm is 6.39 s, 15.66 s, 3.44 s, 15.06 s, 8.02 s, 167.12 s, 180.88 s and 61.04 s. Experimental results show that the proposed incremental attribute reduction algorithm of positive region in interval-valued decision tables is efficient.

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.

For the sensitivity of the portal vein data to classical liver functional segmentation method, a liver segment method based on hierarchical vascular tree combining with the Couinaud theory and portal vein distribution characteristics is proposed. Firstly, liver and vessels are extracted from the abdominal CT image by image segmentation and skeletonization methods. Secondly, secondary subtree set was determined through statistical analysis on average radius of vascular branches, so as to divide the secondary subtree set into several different classes by k-means++ clustering algorithm according to their own blood-supply area. Thirdly, a nearest neighbor segment approximation algorithm was used to segment the liver into parts. Finally, the internal anatomical structure of liver and its vascular system was demonstrated using three-dimensional visualization technology, and then making annotations on liver segments to extract clinical interest information. Experimental result shows that the method can obtain good results when vascular tree contains plenty branches and complex structure. Furthermore, for considering the impact of major secondary branches, the final liver segment distribution and attribute results are in line with the Couinaud liver segment theory.