Ordered Fuzzy Numbers Applied to the Implementation of a Fuzzy PID Controller

The authors presented ordered fuzzy numbers arithmetic applied to the design of a PID controller. The arithmetic allowed the implementation of fuzzy control without the need to use a rule block and related inference operations. This approach is natural and does not require an expert rule set. With this approach, no time is wasted for extraction of external rules and the control takes place in real time. It is worth noting that the order present in the OFN notation carries additional information about the behavior of a given phenomenon. This order informs about the process change trend in the process of processing input signals by arithmetic operations. The final part of the paper presents the defuzzification methods appropriate for the arithmetic applied, which were used to convert fuzzy numbers into real values of the signal controlling a given object according to the PID mechanism.