An Algorithm for Identifying the Dichotomous Convolution Graph of Risk Components in Complex Organizational Systems Based onIts Expert-Defined Hierarchical Decomposition

Abstract. Most well-known methods and algorithms for assessing the risks of complex organizational systems are based on the independence assumption of aggregate risk components. At the same time, in practice, risks are often interrelated, i.e., a change in one risk entails a change in others. Therefore, when assessing the aggregate risk of organizational systems, their complexity––the presence of numerous interrelated risks––should be taken into account. This can be done using the integrated rating mechanism as a multicriteria assessment method. In the classical version, its components––the binary trees of criteria and the logical convolution matrices of their values––are set by experts. However, in many cases, experts cannot agree on the structure of the integrated rating tree. In such practical situations, formal methods for synthesizing the tree structure considering the system specifics are in demand. Even if a method yields a nonunique solution, it will ensure the latter’s logical validity, and the results can be used in practical tasks. In this paper, the mechanism is extended by replacing the binary integrated rating tree with the dichotomous convolution of aggregate risk components of complex organizational systems, based on its expert-defined decomposition. An algorithm for identifying the dichotomous convolution graph of risk components is proposed, including construction rules and verification criteria. The theoretical results are applied to construct a system for assessing the risk of an aviation accident.

Keywords: risk assessment, aggregate risk, integrated rating, binary tree, dichotomous convolution, hierarchical risk decomposition, risk of an aviation accident.