## 5 Conclusions
It is well known that, in the general case, the number of vectors in orthants will decrease with an increase in the number of indicators used in the classification rule. This reduces the generalizing ability of the method. To overcome this drawback, it is necessary to increase the number of patients in the training sample with an increase in the number of indicators. The second justification of the classification result is performed using a logical function. Each connection of the decision rule corresponds to an orthant, which is determined by the parameters of a patient with an indolent form of the disease (class \(\omega_{1}\)). Logical rules (8)-(12) consist of 2-3 conjunctions, which in the learning process are selected from 124 conjunctions of the training sample. Each of the conjunctions participating in the above rules corresponds to an orthant containing a sufficiently large number of vectors of the class \(\omega_{1}\). Thus, each logical rule (8)-(12) generalizes well enough the knowledge contained in the training sample of patients. Therefore, solution (8) gives a rule that determines the balance point between sensitivity and specificity. When (8) is fulfilled, the probability of successful classification of patients with indolent form is \(U(\mathbf{x})=0.765\) with the probability of misclassification of patients with aggressive form \(V(\mathbf{x})=0.235\). If this rule is not met, then we obtain a solution at which the probability of correct classification of patients with an aggressive form of \(1-V(\mathbf{x})=0.765\) with an erroneous classification of patients with an indolent form of \(1-U(\mathbf{x})=0.235\). Equations (9)-(12) give higher levels of probability of successful classification for patient subgroups. The data of 341 case histories of operated patients with indolent and aggressive forms of prostate cancer were analyzed. Analysis of preoperative and postoperative data revealed the dependence of the form of prostate cancer on preoperative data. This relationship is used to classify the form of the disease. For this, it is required to indicate to the algorithm either the threshold value of the probability of successful classification of patients with an indolent form of the disease or the threshold value of the probability of misclassification of patients with an aggressive form of the disease. As a result, we can draw two conclusions about the application of the method of monotonic functions to the problem of classifying the form of prostate cancer according to the data before treatment: (1) The satisfactory quality of the solution allows us to consider the uniformity model. as adequate to the problem being solved; (2) The above examples (8)-(12) show that the calculated logical rules are quite simple and easily interpreted from the point of view of preoperative indicators of the form of the disease. Conceptualization, V.G., N.S., and A.K. ; methodology, V.G. and E.Y. ; software, A.D. and K.P. ; validation, S.P., N.S., and B.A. ; formal analysis, V.G., S.P., N.S., and B.A. ; investigation, V.G., K.P. and E.Y. ; resources, N.S. and B.A. ; data curation, N.S. and B.A. ; writing--original draft preparation, V.G. ; writing--review and editing, A.D., K.P., and S.P. ; visualization, K.P. ; supervision, V.G. ; project administration, V.G. and A.K. ; funding acquisition, V.G. All authors have read and agreed to the published version of the manuscript. The study was conducted at the Institute for Information Transmission Problems, Russian Academy of Sciences, and partially supported by the Russian Foundation for Basic Research, project no. 20-07-00445. The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Ethics Committee of P.A. Hertzen Moscow Oncology Research Institute (branch of the NMRRC, MHR) (protocol code 01-12-567 on 15 March 2021). Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.