On the Importance of Considering Measurement Errors in Fuzzy Logic Systems for Scientific Applications with Examples from Nuclear Fusion

In practically all fields of science, measurements are affected by noise, which can sometimes be modeled with an appropriate probability distribution function. The results of measurements are therefore known only with uncertainties that sometimes can be significant. In many cases the noise source is independent of the system to be studied and the quantities to be measured. In this paper, a numerical approach to handle statistical uncertainties, due to an independent noise source, in a fuzzy logic system is developed. Numerical analysis and various tests with a benchmark show how statistical error bars can be interpreted as an independent "axis of complexity" with respect to the fuzzy boundaries of the membership functions. The uncertainties in the inputs can be transferred to the output and handled separately from the system intrinsic fuzzyness. The main advantages of this independent treatment of the measurement errors are shown in the case of a binary classification task: the regime confinement identification in high-temperature tokamak plasmas. Significant improvements in the correct prediction rate have been achieved with respect to the classification performed without considering the error bars in the measurements.