Publication Date



Technical Report: UTEP-CS-22-41


Fuzzy control methodology transforms the experts' if-then rules into a precise control strategy. From the logical viewpoint, an if-then rule means implication, so it seems reasonable to use fuzzy implication in this transformation. However, this logical approach is not what the first fuzzy controllers used. The traditional fuzzy control approach -- first proposed by Mamdani -- transforms the if-then rules into a statement that only contains and's and or's, and does not use fuzzy implication at all. So, a natural question arises: shall we use logical approach or the traditional approach? In this paper, we analyze this question on the example of a simple system of if-then rules. It turns out that the answer to this question depends on what we want: if we want the smoothest possible control, we should use logical approach, but if we want the most stable control, then the traditional (Mamdani) approach is better.