## 3 Results
### Discussion of Results  
The methods proposed in the work for the development of mathematical models of technological objects functioning in conditions of indistinctness of the initial information allow us to build fuzzy models with clear input and fuzzy output parameters of the object (FM method) and linguistic models with fuzzy values of the input and output parameters of the object (LM method). The method for constructing fuzzy models is based on the use of methods of sequential inclusion of regressors (for structural identification of the model) and a modified least squares method using a set of level \(\alpha\) (for identification of model parameters). The method of constructing a linguistic model is based on the use of logical rules for conditional inference and linguistic variables that describe the input and output parameters of the object. To determine the volume of hydrogenate, i.e., of the target product from the outlet of the hydrotreating reactor R-1 using the methods of sequential inclusion of regressors and least squares on the basis of the experimental statistical data package and the REGRESS software package, a statistical model was built that makes it possible to determine the volume of hydrogenate from the outlet of the reactor depending on the input, operating parameters \(x_{i},\ i=\overline{1,5}\). Since the initial information for assessing the quality of the produced hydrogenated product is characterized by indistinctness, a systematic approach using the methods of expert assessments and theories of fuzzy sets was applied to construct models for assessing the quality of the hydrogenated product. An expert assessment of the influence of the input and operating parameters on the quality parameters of the hydrogenated product was carried out. Then, processing the collected data and expert information using the fuzzy modeling method proposed in Section 3.1, the structure of fuzzy models was identified to describe the product quality of the hydrotreating reactor R-1 in the form of fuzzy multiple regression Equation (7). The main disadvantage of the methods used in practice for calculating furnaces is that they determine only the integral indicators of the heat transfer process, and allow the possibility of heating the local tubes of the furnace. To eliminate this drawback, it is proposed to apply the zonal method, which is based on replacing integral-differential  
Figure 7: Inputs–output surface in the SurfaceViewer window. equations that describe the process of heat transfer by a system of algebraic equations. The zonal method of calculating the furnace can provide sufficient accuracy; to increase the accuracy, it is necessary to increase the number of zones. However, this method is rather complicated and the collection of the necessary information for its application in practice is also difficult. Therefore, to simulate the operation of the F-101 hydrotreating furnace, it is proposed to use an analytical method based on the joint solution of the heat transfer and heat balance equation to quickly obtain the necessary information and results. Statistical models were built that make it possible to determine the output of the hydrotreating furnace: the volume of the mixture of raw materials and gas and the temperature of the outlet flow from the furnace, in the form of nonlinear regression Equation (8). To determine the optimal temperature of the hydrotreating process, based on expert information and a logical rule of conditional conclusions and a rule base, a linguistic model was built that estimates the optimal temperature depending on the quality of raw materials and furnace pressure. Based on the simulation of the operation of the furnace and the hydrotreating reactor of the reactor and the analysis of their results, it is possible to select the optimal operating mode that provides the effective values of the optimization criteria, for example, maximizing the hydrogenated product yield from the R-1 reactor while ensuring the required quality indicators.