A Mathematical Model for Representing the Related Operator Professional Activities and Their Diagnostic Assessments Based on the Quantum Representations

This study presents a mathematical model of related activity designed to obtain comparative assessments of the performance of complex technical systems operators, representing their activity through a probability matrix of transition between the performed elementary operations. The feasibility of this model is due to the high efficiency of quantum spectral analysis of transition probability matrices in combination with quantum filtering when solving classification problems. The alternative approach, which relies on the assessments of mutual likelihoods, constructed using transition probability matrices, reveals substantially less significant differences in operators’ activities and yields to the method based on quantum representations in completeness, efficiency, and quality of the obtained results. This study showed that with a sufficiently large volume of empirical data, even a one-time manifestation of some regularity indicates its presence and the regularity index value can measure the reliability of such a conclusion. The presented mathematical apparatus provides higher efficiency than other approaches, obtaining diagnostic conclusions using empirical data of much smaller volume and extracting more helpful information.