Methods of local and integral multilevel aggregation estimates of objects measured in different types of scales

In the tasks of multi-criteria assessment and selection of objects with a multilevel structure, the initial data characterizing the objects are usually measured in different scales. In this regard, the use of additive convolution for the end criteria of a hierarchical tree reflecting the multilevel structure of objects is correct only for estimates of objects represented or transformed to a single homogeneous scale. The article introduces the concept of weight in the quantitative scale of the relations of the criterion (k-1)-th level of the hierarchical tree, determined by the sum of the weights of the subcriteria of the k-th level. In this case, the application of the procedure for calculating global normalized weights, which are commonly called coefficients, at each level of the hierarchy through a multiplicative convolution of local coefficients lying on the path from the root vertex is correct. The proposed method of local aggregation of estimates of objects with a multilevel structure has an important property, namely: the adequacy of the ordering of objects at any vertex of the hierarchical structure of criteria for calculating aggregated estimates in a quantitative, ordinal (rank) scale. It is shown under what conditions the integral method of aggregated estimates based on global coefficients of the end criteria coincides with the local one. The advantages of the local method are visibility, the ability for analysts to understand and control intermediate results, and greater objectivity of calculated estimates at the root vertex of the hierarchical tree. The essence of the methods and their comparison is shown by the example of a multi-criteria evaluation of information materials.

hierarchical tree, local and global weights of criteria, local data aggregation, scale transformation