Objective: To estimate the epistemic (or fuzzy) uncertainty, arising due to limited data samples in the measurement of the output factors (OF) of the small fields using Fuzzy Set Theory (FST). Methods: EBT3 film samples of size 50 × 50 mm were used for the measurement of the OF of stereotactic radiosurgery (SRS) cones of size 4, 6, 7.5, 10, 12.5 and 15 mm diameter, normalized with respect to the output of 100 × 100 mm open field size. Three measurements were done per cone/field size. Red color channel was chosen for the dosimetry purpose, net optical density (NOD) was converted to the dose using non-linear relation. To estimate the epistemic uncertainty associated with the measured OF due to limited number of data samples, a triangular fuzzy number (TFN) was assumed as the fuzziness in the dose delivered by the individual SRS cone/field. Uncertainty in the OF was estimated by applying the Fuzzy Vertex Method (FVM). The membership functions of the OF were constructed for each cone size and the nature of the uncertainty in the OF of the cones was expressed in the terms of its fuzziness. For the sake of completeness of the study, the statistical uncertainty involved in the procedure has also been calculated. Results: The statistical and fuzzy uncertainties in the measurement of OF of cones range from 3.28 to 6.25% and 2.58 to 5.44% respectively. The smallest cone of 4 mm has the largest values of statistical and fuzzy uncertainties. The membership functions of the OF for the studied cones were triangular in nature. Conclusions: The epistemic uncertainty arising due to limited number of data samples holds a significant fraction of the prescribed dose, and therefore, should not be ignored in the total uncertainty estimation. Advances in knowledge: This study highlights the significance of epistemic component of measurement uncertainty arising out due to the insufficient/limited number of measurements of a quantity.
Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory
