Fuzzy control with fuzzy inputs: the need for new rule semantics

The standard computation taking place in a fuzzy logic controller proceeds from crisp inputs and via the consecutive steps of fuzzification, inference, and defuzzification computes a crisp control output. However, this computational practice simplifies to an extent the actual developments taking place in the closed loop. In reality, the knowledge about the current values of the controller input is very often available via sensory measurements. In this case, one has to take into account the negative side effects that come up with the use of sensors, in particular the presence of noisy measurements. In the paper the authors consider one particular way of dealing with noisy controller inputs, namely transforming the noise-distribution into a fuzzy set and then feeding back the so obtained fuzzy signal to the controller input. Adopting this approach requires that the shape of the input fuzzy signal should be reflected as much as possible in the output fuzzy signal so that important noise characteristics are preserved. In the paper the authors describe the requirements on the shape of the fuzzy output signal given a certain fuzzy input signal and show that the existing semantics for fuzzy IF-THEN rules do not satisfy these requirements. The authors propose new semantics for such rules which together with max-min composition produces the desired results