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 a ? and a + ", 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 a ? and a + ". 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 diierent membership functions to represent the same uncertain statements, and diierent functions lead to diierent results. What membership function to choose? In the present paper, we show that under some reasonable assumptions, Gaussian functions (x) = exp(?x 2) are the most adequate choice of the membership functions for representing uncertainty in measurements. This representation was eeciently used in testing jet engines for airplanes and spaceships.