Applying the Theory of Multi-Operations to Building Decision-Making Systems with a Large Number of Uncertainties

This article is devoted to the practical application of multi-operations theory to the construction of decision-making systems and the description of the subsequent research results. Unlike classical multi-valued and fuzzy logic, where events are described by only two logical values, namely, “true” and “false”, when there are various types of uncertainty between these two states, the theory of multi-operations can be used to describe events using a larger number of logical values for the uncertainties between these states. This article demonstrates a new approach to processing input information using rank 3 multi-operations, i.e., considering input information for a set of three logical values and five values of uncertainty. This approach allows for saving time and resources when forming a subject area model for decision-making systems and when working with specific users. The application of this approach is illustrated in the article by using the example of determining the area of human disease. When testing this system, which is built on the basis of rank 3 multi-operations, we show that applying multi-operations theory allows for significant expansion of the range of accepted decisions; this makes the system more flexible for the construction of human–machine interfaces and organizes the integration of efforts in the development of humans and machines with a common goal.