An Alternative Fuzzy Logic Inference Method on the Example of a PID Controller

This paper presents a different approach to the inference process of a fuzzy controller. An important trait of the approach is the use of an OFN (ordered fuzzy numbers) property and an arithmetic apparatus. The solutions of inference processing are based on the work by Mamdani or Takagi-Sugeno, which share a common feature, a mechanism of a rule base. The approach postulated in this work does not feature a classic distribution; it only applies characteristic OFN properties using an arithmetic apparatus. The problem of system control is presented as a mathematical formula in which OFN are substituted. The approach simplifies the operations processed in the controller, an important element for which is the mathematical model of the process discussed in the paper. The results are interpreted within the area of interest of the given system. As an example, a discussion of the possible solutions of a PID controller for OFN is provided.