Special attention should be paid to the fact that railway transport management systems, as well as complex systems in general, are characterized by fundamental inaccuracy and uncertainty in both data and management decisions. This makes it possible to attribute such systems from a mathematical point of view to the class of incorrect tasks and makes it possible to evaluate the quality of technical and managerial decisions in a different way. In this case, the promptness of the decisions taken plays a greater role than their optimality, understood in a strict mathematical sense. This quality is an important property of intelligent systems [14,15,16].
In recent decades, there has been an active development and research of formal methods of working with uncertain data. Until recently, probability theory was the main instrument for accounting for uncertainty. However, the axiomatic limitations associated with it do not allow us to adequately apply probabilistic approaches to solving many important problems in which uncertainty has a different nature or properties. For example, the uncertainty of the events under consideration does not always have a frequency character, objective difficulties often arise with the formalization of a specific probability space, in many cases assumptions about the additive nature of a probability measure are difficult to explain, and sometimes simply unacceptable. For these reasons, at present, along with probability theory with its developed mathematical apparatus, new theoretical approaches to the description of uncertainty and incompleteness of information are actively being investigated. Here, first of all, we should mention the Dempster – Shafer theories, possibilities, interval averages, monotone measures. These theories have less rigid axiomatics, which allows, along with the frequency interpretation of events, to describe events whose uncertainty may be subjective (for example, the probability is determined by a number reflecting the subjective degree of confidence in the event), or in which the number of observed realizations does not allow obtaining reliable conclusions in a statistical sense.
An important area that can have real practical application in the railway industry when creating ITS is the development of expert systems, i.e. computer programs that can fully or partially replace a specialist expert in some, as a rule, rather narrow problem area. Expert systems began to be developed by artificial intelligence researchers in the 1970s, and already in the 1980s they found their commercial applications. Expert systems function mainly together with knowledge bases, which are a set of facts and rules of logical inference in the chosen subject area of activity. This allows, in general, to model the behavior of experienced specialists in a certain field of knowledge using logical inference and decision-making procedures.