Investigation of Hierarchical Fuzzy Inference Systems, when Obtaining Integral Estimates of the Analyzed Objects

The purpose of this paper is to study the patterns of the formation of output values in hierarchical systems offuzzy inference. Hierarchical fuzzy inference systems (HFIS) are used to aggregate heterogeneous parameters during the assessment of the state of various elements of complex systems. The use of HFIS allows avoiding the "curse" of the dimension associated with a strong increase in the number and complication of the structure of the production rule, which is characteristic of conventional fuzzy inference systems (FIS), which aggregate the results of interaction of different values of input variables in one knowledge base. As part of the research, numerical experiments were carried out to study the features of the formation of output patterns in HFIS, based on FIS using the Mamdani and Takagi-Sugeno algorithms. As a result of the experiment, it was shown that the output values of the studied HFIS tend to be grouped in the region of fixed values, and the output pattern itself acquires a stepwise character. The revealed property allows using HFIS to distribute the objects of the analyzed sample into groups of states. This property can be used to solve problems of distributing objects into groups in conditions when it is difficult to form a training sample for machine learning methods, but at the same time there is knowledge of the expert group about the features of the functioning of the object of research. Additionally, the paper investigates the features of the formation of output patterns depending on the parameters of the membership functions describing the input variables in HFIS, which are based on FIS using the Mamdani algorithm and HFIS, which are based on FIS using the Takagi-Sugeno algorithm.