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On the importance of considering Measurement Errors in a Fuzzy Logic System for scientific applications in Nuclear Fusion

In Magnetic Confinement Nuclear Fusion, as in practically all fields of science, the measurements are affected by noise, which can sometimes be modelled with an appropriate probability distribution function. The results of the measurements are therefore known only with uncertainties which sometimes can be significant. In many cases the noise sources is independent from 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 the 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.
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