A t-norm based fuzzy approach to the estimation of measurement uncertainty

From a metrological point of view, a measurement process rarely consists in a direct measurement. For example, the output performed by a DSP-based instrument can be considered as an indirect measurement. The acquired samples of input signals represent the single direct measurement result, while the measurement algorithm performed by DSP-based instrument represents the indirect measurement result which is a function of the previous ones. Everyway, no matter what kind of instruments we are using in our process, we need to know how the uncertainty propagates in measurement processes. In order to express the measurement result with its associated uncertainty, we have to meet the recommendations of the Guide (1999). In this paper we propose the use of fuzzy intervals to describe both systematic and statistical effects on the distribution of measurement results. To avoid the inconvenience of not reducing the uncertainty with the averaging operations of series of data, we'll use random fuzzy variables to describe the single measurement. The data processing of the measurements results are performed using the extension principle based on Dombi's t-norm.