Modelling and parametric optimisation of an expert survey using slice matrices

Abstract

The article considers the creation and application of situation centers at internal affairs bodies under conditions of increasing complexity and heterogeneity of threats arising in modern society. The need to solve diverse tasks in order to ensure public safety and protect public order requires the engagement of experts. The article deals with the problem of conducting and processing the results of an expert survey of pairwise comparison of alternatives in the situation centers of internal affairs bodies using a previously developed algorithm based on slice matrices. We suggest that the parameters for optimizing the pairwise comparison should be the choice between speed and accuracy, depending on both the number of objects being compared by one expert and the total number of alternatives being compared. The problems relating to the parametric optimization of the expert survey were formulated. Using information theory and well-known statements about the amount of information and the entropy, we developed an approach that allows taking into account the information losses occurring when forming slice matrices for an individual expert. In order to reduce the number of pairwise comparisons in relation to the total number of pairs of alternatives, we developed an approach that allows evaluating the gain in the speed of conducting an expert survey using slice matrices. A generalized conclusion is made about the numerical equality of speed and information loss when using slice matrices. The article presents the results of a computational experiment carried out to determine the speed and loss of information when conducting an expert survey using slice-matrices. In addition, an example of the dependence of the optimization parameters on the total number of compared alternatives and the dimensionality of the slice matrices is given. A conclusion is made about the choice of the optimal value of the parameters for conducting an expert survey.