Open AccessMETHOD OF SYNTHESIS OF THE INTEGRATED ASSESSMENT SYSTEM
Author(s) -
В.Н. Бурков,
И. В. Буркова,
А. В. Щепкин
Publication year - 2020
Publication title -
vestnik ûžno-uralʹskogo gosudarstvennogo universiteta. seriâ, kompʹûternye tehnologii, upravlenie, èlektronika
Language(s) - English
Resource type - Journals
eISSN - 2409-6571
pISSN - 1991-976X
DOI - 10.14529/ctcr200407
Subject(s) - row , vertex (graph theory) , set (abstract data type) , tree (set theory) , matrix (chemical analysis) , variety (cybernetics) , row and column spaces , mathematics , convolution (computer science) , task (project management) , dimension (graph theory) , computer science , algorithm , discrete mathematics , combinatorics , statistics , artificial intelligence , graph , materials science , management , database , artificial neural network , economics , composite material , programming language
Systems of complex estimation (CO) based on a dichotomous tree of criteria and a set of criteria convolution matrices (generalized criteria) are widely used in the evaluation of a wide variety of ob-jects. Purpose of the study. To build a CO system for a given set of criteria, you need to solve two problems: 1. To choose the structure of the dichotomous tree of criteria. 2. To define matrix convolutions of pairs of criteria (generalized criteria) at each vertex of the tree (except for hanging ones). The article deals with the second problem, i.e. the problem of determining matrices the criteria convolution. In practice, this task is often solved based on expert opinions. Materials and methods. Let us assume that there are a set of options (a variant is a set of criteria estimates) and experts have defined complex estimates for each option from this set. The task is to define matrix convolu-tions at each vertex of the tree such that the CO of each variant in the resulting system CO is equal to the EXPERT estimate. The paper defines a class of unified CO mechanisms that meet the following conditions: 1. All matrices of the unified complex estimation mechanism have the same dimension. 2. For any matrix all rows are different and all columns are different. 3. All matrices are monotonous in rows and columns; 4. If all the variant scores are equal to a certain score, then the complex score is equal to this score. Results. Two cases are considered. In the first case, experts can give estimates of options with any set of criteria estimates. In the second case, experts can give a CO of only complete options, that is, options that contain estimates of all criteria. For the first case, an efficient algorithm with an estimate of computational complexity of the order of lm2 is proposed, where l is the number of crite-ria, and m is the number of gradations of the rating scale. The algorithm makes significant use of the 4 property of unified mechanisms. For the second case, we propose a method for solving the problem by constructing “top-down” matrices, i.e. constructing a matrix for the root vertex, then for adjacent ones, and so on. Conclu-sion. Thus, the paper proposes algorithms for the synthesis of unified mechanisms for complex eva-luation, in which the number of required expert options is minimal.