APPLICATION OF max-min COMPOSITION OPERATION IN SOLUTION OF THE IDENTIFICATION PROBLEM OF FUZZY SYSTEMS

Abstract

The max-min composition operation is a fundamental tool in fuzzy set theory. In particular, it plays an important role in solving the problem of identification of fuzzy systems. In the study of the identification problem of fuzzy systems, the identification solution involves determining the fuzzy relationship that best models the relationship between input-output fuzzy sets based on the observed data. In this work, the application of the max-min composition operation is envisaged in solving the problem of identification of fuzzy systems described in the form of fuzzy relational equations, and an identification algorithm is built based on the rule base. The goal is to more adequately describe the process of solving the problem of identifying fuzzy control systems described in the form of fuzzy relational equations by applying the max-min composition operation. As a result of an objective assessment of the results of fuzzy control that satisfy the desired goals and conditions, control commands are determined as a set of fuzzy values within their values. Appropriate control rules are selected based on the prediction results in accordance with each control command. In this work, dynamic processes are analyzed in three forms: deterministic, stochastic, and fuzzy. Based on the methods of constructing and identifying fuzzy models, it is concluded that it is necessary to develop a relatively adapted fuzzy TSK difference model construction and identification methodology for describing dynamic models under uncertainty. The form “Fuzzy TSK – difference” is a model, which consists of a set of production rules with fuzzy sets on the left side and r,s-ordered difference equations on the right side. The article uses a practical inference method based on the system of implicative fuzzy rules and fuzzy inputs. The basis of fuzzy logical inference, which is composed in the form of fuzzy sets using fuzzy operations and a fuzzy knowledge base, is L. Zadeh's composition rules. The sum of differences was calculated according to the max-min composition operation and the minimum value of the J criterion was found. According to the conducted studies, it was found that the minimum criterion value corresponds to the max-min composition operation.