Real data obtained from measurement processes are not precise numbers or vectors, but more or less non-precise, also called fuzzy. This uncertainty is different from measurement errors and has to be described formally in order to obtain realistic results from data analysis. A real life example is the water level of a river at a fixed time. It is typically not a precise multiple of the scale unit for height measurements. In the past this kind of uncertainty was mostly neglected in describing such data. The reason for that is the idea of the existence of a “true” water level which is identified with a real number times the measurement unit. But this is not realistic. The formal description of such non-precise water levels can be given using the intensity of the wetness of the gauge to obtain the so called characterizing functions from the next section. Further examples of non-precise data are readings on digital measurement equipments, readings of pointers on scales, color intensity pictures, and light points on screens.