Evaluation of complex systems: multicriteria approach

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The quality of object functioning is evaluated by a set of properties that have a quantitative expression (quality criteria). The selection of object properties is carried out by the decision maker (DM). This selected object properties is a decomposition, resulting in a hierarchical structure. In decision theory the case when a multicriteria task is represented by a two-level hierarchical system is developed most thoroughly in great detail. Here, the problem of evaluation (composition of criteria) of a simple object is usually solved using the mechanism of a single scalar convolution of a vector criterion. The numerical value of the convolution is an assessment of the quality of the functioning of this object as a whole. But even with a three-level hierarchy, the object is considered as complex and its evaluation requires other approaches. It is shown that any problem of vector evaluation of an object can be represented by a hierarchical system of criteria obtained as a result of decomposition of the objectʼs properties. With hierarchical decomposition of object properties, the number of levels depends on the required depth of decomposition. Usually they brought to such properties that have a quantitative expression (called criteria). The difficulty lies in the fact that for each initial property, the depth of decomposition can be different. At the lower level of the hierarchy, the object (alternative) is evaluated by individual properties using the initial vector of criteria, and at the upper level, the object as a whole is evaluated by means of the composition mechanism. The central problem here is the problem of composing criteria by hierarchy levels, which is solved by the method of nested scalar convolutions. The necessary and sufficient conditions for the vector estimation of an object are considered.