**6. Conclusions**

This article analyzed the foundations of the future methodology for synthesizing the risk of functional smart expansive systems, taking into account the need to consider the balance between its constituent subsystems: production, development potential and regulation. We propose considering risks as "development anti-potentials" that slow down the reproduction speeds of the entire system. The concept of the geometric integral "antirisk" is introduced, resulting from the concept of "difficulties in achieving the goal". Thus, the conceptual definition of risk as the influence of uncertainties on the achievement of the goal of smart expansive systems is formalized.

To assess private risk factors included in the integral risk, we propose a method of vector compression. The idea to build compatible reference solutions, which form the basis for the developed method, represents an alternative to pairwise comparison in the method of analysis of hierarchies and the method of analytical networks.

Further to this, we propose an approach to processing partial matrices of pairwise comparisons, which makes it possible to minimize the disadvantages of the existing methods for working with similar matrices, especially for matrices of large dimensions. The principles of handling pairwise comparison matrices by describing their upper and lower boundaries have been investigated. The developed vector compression algorithm allows us to obtain the weights of compared objects on the basis of matrices of pairwise comparisons containing omissions, without fully restoring the matrix of pairwise comparisons, and also allows us to obtain the weights of given upper and lower boundaries through comparative assessment of pairs of objects.

This paper is not a standalone work capable of covering all issues and presenting the variety of smart expansive systems. These will undoubtedly be the topics of further

research. To give an example of where future studies may take us, the smart expansive system in this paper was considered in a linear approximation and stationary case. Beyond the scope of the article, a question must also be raised about the behavior of an intelligent expansive system in a "non-stationary state", where oscillatory processes (and maybe chaos) may occur. Moreover, the uniqueness of the approximation we chose has not been proven, and the option of using the vector compression method for upper and lower bounds in cases of restrictions imposed on the coefficient (greater than/less than zero) for fuzzy definition of the original matrices has not been considered. We plan to investigate all these and many other avenues in the future.

The proposed method could become an important element in the algorithmic provision of expert advising systems to support decision-making on the managemen<sup>t</sup> of smart expansive systems, provided there is an appropriately organized procedure for selecting experts to be involved in the assessment of solutions.

**Author Contributions:** Conceptualization, A.B. and N.Z.; methodology, A.B.; software, A.R.; validation, A.B., N.Z. and N.K.; formal analysis, N.K.; investigation, N.Z.; data curation, N.Z.; writing— original draft preparation, A.B.; writing—review and editing, A.B.; visualization, A.R.; supervision, N.Z.; project administration, A.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
