## 1 Introduction  
Machine-learning methods are widely used in modern medicine. These methods have the potential to be used to extract knowledge from medical data to diagnose a disease, determine the severity of a patient's condition, choose a treatment method, and predict their condition after treatment [1, 2, 3, 4]. Most machine-learning methods are based on general statistical classification models. However, there are problems of diagnostics and forecasting, the features of which are not taken into account in these models. These include the tasks of medical diagnostics with a monotonous relationship between prognostic and predicted indicators: the stronger the deviation of prognostic indicators from the norm, the more serious the predicted degree of the disease. Therefore, for example, in the works [5, 6] to determine the severity of the patient's condition, a model was proposed in which it was assumed that an increase in the deviation of any of the indicators of the patient's condition from the norm, all other things being equal, increases or does not change (but does not decrease) the severity of the disease. Taking into account the property of monotonicity inherent in such problems would facilitate their more efficient solution.  
To solve diagnostic problems with a monotonic relationship between prognostic and predicted indicators, we have developed a method of monotonic functions. In this paper, we consider the method and its application to select one of two types of surgery for prostate cancer based on preoperative data. Prostate cancer (PCa) is the second most common malignant neoplasm (after lung cancer). Globally in 2018, it amounted to 1,276,106 new cases and caused 358,989 deaths (3.8% of all cancer deaths in men) [7]. The choice of appropriate treatment tactics is based on the results of pretreatment staging of PCa.  
Research on the indicators of prostate cancer is developing intensively. Studies aimed at identifying the specific features of PCa have identified the diagnostic potential of separate indicators of the disease. These studies have shown the need for the development of multivariate models for diagnosis and determination of the stage of the disease, as well as for the prognosis and choice of treatment tactics. Research related to the development of the Prostate Health Index (PHI) is a very successful example of aggregating prostate cancer indices [8; 9; 10]. The cycle of works on the Prostate Cancer Risk Assessment Index (CAPRA) is widely known [11; 12; 13]. The CAPRA Index was designed to facilitate the classification of disease risk when conducting clinical assessments of the likelihood that a given tumor will recur after treatment, progress, and be life-threatening, according to pretreatment data. One of the urgent problems when choosing the type of surgery is the classification of indolent and aggressive forms of PCa in patients with the initial stages of the tumor process. The problem of the classification of patients with indolent and aggressive forms of PCa before treatment was considered in [14; 15; 16; 17; 18; 19]. In these works, the logistic regression method was used to solve the problem. Five indicators were used for classification. Based on cross-validation data, the algorithm identifies a group of 55% of patients with aggressive PCa in the absence of patients with indolent PCa status. These forms of the disease are ordered. The aggressive form of the disease refers to a more severe form, which is characterized by the presence of a more common tumor process. To solve this problem, we propose to use a new machine-learning method of binary classification, which we called the method of monotonic functions.  
We consider the basics of the method of monotonic functions in Sections 2 and 3. Section 4 describes the experimental modeling and the result of applying the method to the problem of classifying patients with indolent and aggressive PCa.