Determination of the Optimal Option of Book Usage Based on the Linear Convolution of Criteria

Abstract

The peculiarities of the book product usage after its release are considered, in particular, a number of factors influencing the level of book usage with the highest priority are presented: place of residence; availability (accessibility) of literature; family (family role); content, book subject. The selection of factors from the total set is carried out according to the Pareto principle, according to which only the most priority factors are taken into account, and factors with significantly lower indicators are rejected. The graph shows the difference in the weight values of the selected factors.

Three alternative options for forming the level of book usage are presented. The degree of importance of each factor is assessed according to three alternatives. For convenience, the obtained data are presented in a table. A matrix of pairwise comparisons of the Pareto set factors is formed. For this purpose, the scale of relative importance of objects according to Saaty is used, which allows the expert to compare the preference degree between factors with the help of specified numbers. One indicates the equal value of objects, and nine indicates the absolute superiority of one factor over another. The remaining values are intermediate. As a result of processing the matrix of pairwise comparisons, the components of the main eigenvector, which are the weight values of the Pareto set factors in relation to the three projected alternatives, are established and normalized. The normalization criteria are also defined: the maximum eigenvalue of the main eigenvector of the matrix of pairwise comparisons, the consistency index, the consistency ratio. The normalization criteria are within the norm, which indicates the adequacy of the problem solution.

Alternatives are compared for each factor. The normalization criteria and utility functions are calculated. Multi-criteria utility assessment are formed for three designed alternatives. The best alternative for forming the level of book product usage is chosen according to the maximum value of the utility assessment.