Estimation of Uncertainty in Measurement by means of Type-2 Fuzzy Variables

Uncertainty modelling in measurement represents a crucial task since the final result of a measurement process cannot be expressed by a single value, but by a distribution of values over an interval within which the measurements lie with a given confidence level. A classical Type-1 fuzzy set could be the natural choice for uncertainty model, since a Membership Function (MF) intrinsically embeds the concepts of confidence interval and confidence level. Moreover, from computational aspects, working on fuzzy sets is much more easily than a Montecarlo simulation, that is actually the recommended approach. However, both the approaches need reliable and specific assumptions on the probability distribution of the input variables. So, in many practical cases, a Type-2 fuzzy set is needed in order to overcome this problem. In this paper, we will provide a full description of how a Type-2 MF can be built in order to model the uncertainty of a variable and how to evaluate uncertainty propagation through a generic function. A practical example of this representation will be also provided and compared with a Montecarlo simulation.