Type-2 Fuzzy Sets for Modeling Uncertainty in Measurement

A correct representation of uncertainty in measurement is crucial in many applications. Statistical approach sometimes is not the best choice, especially when the knowledge of the measurement process refers only to the support of the values and does not allow a correct assumption on the probability density function (pdf) of the measured variable. In this paper we present an approach that uses the concept of generalized fuzzy numbers, namely type-2 fuzzy sets, in order to handle the intrinsic dispersion of the possible pdfs associated to a variable. The relation between our representation and the so called random fuzzy variables (RFV) will be also investigated. The use of this representation allows to easily implement the uncertainty propagation, through a functional model, by working directly on the type-2 fuzzy numbers and by evaluating simultaneously the propagation results for the whole set of confidence levels. Anyway, when a statistical analysis can be performed, the results can be embedded in this generalized representation. Moreover, the new approach allows to assign to the final measurement value a reliable confidence level also in this case, by combining the expanded uncertainty evaluated following IEC-ISO guide recommendations with the type-2 fuzzy numbers associated to the output variable. An example of this representation was provided