## 3 Results
### Results of the Preliminary Data Analysis
Thus, four indicators (L_BV, R_BV, L_TV, R_TV) were selected as the most significant from among all available indicators. Subjects with the same vectors of encoded veins were united into 42 subgroups. For example, subjects 003 has a vector of values of the MSV {259.0; 172.0; 333.0; 159.0}, which was encoded to vector {2; 1; 3; 1}, and subjects 057 has a vector of values of the MSV {216.0; 147.0; 301.0; 140.0}, which was encoded to the same vector {2; 1; 3; 1}. Moreover, there were 8 contradictory examples in the encoded dataset. For example, from Table 3 we can see that subjects 001 and 079 have the same vector of discrete values {3; 1; 2; 1}, but they belong to different groups: AD and CON. To reduce conflict examples, we excluded those subgroups or subjects that had high level of similarity to one group but in fact belonged to another group. The similarity was measured in the System \"EIDOS-Xpro\" by values of the integrated similarity criteria using information model INF3. The \"EIDOS-Xpro\" system, according to both integral similarity criteria \"Semantic stability of knowledge\" and \"Sum of knowledge\" with a value of 99.69% similarity, refers the patient sub007 to the CON groups, i.e., is not ill, while this patient is clinically diagnosed with Alzheimer's disease (Figure 4). Other subjects (Table 4) were excluded in the same way. Subjects 057, 003, 076 and 075 were excluded from the encoded dataset because the vectors {2; 1; 3; 1}, {2; 2; 1; 3} corresponding to them have uncertainty. The training set, after excluding the conflict examples, includes 34 unique, encoded vectors. They corresponded to 63 subjects (patients), which accounted for 78% of the original number of subjects. This training set for identification of the integrated rating mechanism (decision's root) is presented in Table S1. .2.1 The Integrated Rating Mechanism (Decisions' Roots) Identified Based on the Encoded Training Set  
In the previous study [40], we used the identification algorithm proposed in [47], which is applicable to any structure of criteria trees without restrictions on the alphabet used inside the convolution matrix. Removing the restriction on the alphabet used to encode the elements of the convolution matrices, it is possible to approximate the initial data with several functions due to the fact that when gluing equivalence groups, the variability of these gluings arises [48]. As was said above, 15 full binary trees with named leaves are possible for 4 factors. From all possible tree structures in [40], it was proposed to convolve to produce indicators characterizing the left veins with each other, as well as the right ones with each other. This is because veins are paired and participate in the process of blood circulation of the two hemispheres separately and because arteries and veins in each of the hemispheres, and in the brain as a whole, have many collaterals that redistribute blood flow both among themselves at the beginning, within one hemisphere, and then, with a lack of compensatory capabilities within the entire brain (Figure 5). For each criteria tree structure, a few decisions' roots can be identified; one example was presented in [40] (p. 426). The following decision's root (Figure 5) was identified based in the training set presented in Table S2.