Fuzzy logic for reconstructing arbitrary moments of multiplicity distributions

The Identity Method is a statistical technique developed to reconstruct moments of multiplicity distributions of particles produced in high-energy nuclear collisions. The method leverages principles from fuzzy logic, allowing for a more nuanced representation of particle identification by assigning degrees of membership to different particle types based on detector signals. In this contribution, a mathematical framework, based on a multivariate moment generation function, is developed that allows the derivation of the formulas used in the Identity Method in a more robust way. Moreover, within the introduced framework, the Identity Method is easily extended to cope with arbitrarily higher-order moments. The techniques developed here offer significant potential for improving the accuracy of multiplicity distribution analyses in high-energy nuclear collisions. While the primary focus of the work presented is on applications in high-energy and nuclear physics, it can also be applied in other areas where signal identification is probabilistic and data are noisy, such as medical imaging, remote sensing, and various other fields of experimental science.