Gaussian membership functions are most adequate in representing uncertainty in measurements

In rare situations, like fundamental physics, we perform experiments without knowing what their results will be. In the majority of real-life measurement situations, we more or less know beforehand what kind of results we will get. Of course, this is not the precise knowledge of the type 'the result will be between alpha - beta and alpha + beta,' because in this case, we would not need any measurements at all. This is usually a knowledge that is best represented in uncertain terms, like 'perhaps (or 'most likely', etc.) the measured value x is between alpha - beta and alpha + beta.' Traditional statistical methods neglect this additional knowledge and process only the measurement results. So it is desirable to be able to process this uncertain knowledge as well. A natural way to process it is by using fuzzy logic. But, there is a problem; we can use different membership functions to represent the same uncertain statements, and different functions lead to different results. What membership function do we choose? In the present paper, we show that under some reasonable assumptions, Gaussian functions mu(x) = exp(-beta(x(exp 2))) are the most adequate choice of the membership functions for representing uncertainty in measurements. This representation was efficiently used in testing jet engines to airplanes and spaceships.