arXiv subjects

Vitaliy Tsyganok

Publications and source records attributed to Vitaliy Tsyganok.

8 recordsLinked to original sources

arXiv2026

Combinatorial and Sampling Approaches to Determining the Priority Vector from an Incomplete Pairwise Comparison Matrix on the Set of Spanning Trees

This paper considers combinatorial and sampling approaches to deriving a priority vector from an incomplete pairwise comparison matrix. It is shown that the informationally significant combinations of matrix elements are in one-to-one correspondence with spanning trees of the graph induced by the matrix. The combinatorial approach is based on the enumeration of all spanning trees and the componentwise aggregation of the priority vectors derived from them. To reduce computational complexity, a sampling Monte Carlo approach with a sequential stopping criterion is proposed, ensuring a prescribed accuracy for estimating the components of the resulting vector.

math.GM↗

arXiv2026

Stability of Ranking-dependent Pair-wise Comparison Patterns in the Analytic Hierarchy Process

The paper addresses several ranking-dependent decision support methods. Ordinal information on compared objects can be used to improve the quality of expert data during estimation and help reduce the number of comparisons that the experts need to perform. In the paper we compare three incomplete ranking-dependent pair-wise comparison patterns which can be used in the Analytic Hierarchy Process - Best-worst method, Best-Second Best (Top 2) method, and the original maximum difference method. The first two comparison patterns (and respective methods) are incomplete, while the third can be a complete one. We determine conditions under which these three methods can be compared in terms of stability to expert errors. We also present the results of a simulation-type experiment, in which the three methods are compared. The research allows us to define the most stable incomplete ranking-dependent pair-wise comparison pattern and reduce the number of comparisons without loss of credibility of expert session results. The research contributes to algorithmic, cognitive, and applied aspects of decision support in uncertain environments.

cs.AI↗

arXiv2024

Determining adequate consistency levels for aggregation of expert estimates

To obtain reliable results of expertise, which usually use individual and group expert pairwise comparisons, it is important to summarize (aggregate) expert estimates provided that they are sufficiently consistent. There are several ways to determine the threshold level of consistency sufficient for aggregation of estimates. They can be used for different consistency indices, but none of them relates the threshold value to the requirements for the reliability of the expertise's results. Therefore, a new approach to determining this consistency threshold is required. The proposed approach is based on simulation modeling of expert pairwise comparisons and a targeted search for the most inconsistent among the modeled pairwise comparison matrices. Thus, the search for the least consistent matrix is carried out for a given perturbation of the perfectly consistent matrix. This allows for determining the consistency threshold corresponding to a given permissible relative deviation of the resulting weight of an alternative from its hypothetical reference value.

stat.ME↗

arXiv2019

Comparing Efficiency of Expert Data Aggregation Methods

Expert estimation of objects takes place when there are no benchmark values of object weights, but these weights still have to be defined. That is why it is problematic to define the efficiency of expert estimation methods. We propose to define efficiency of such methods based on stability of their results under perturbations of input data. We compare two modifications of combinatorial method of expert data aggregation (spanning tree enumeration). Using the example of these two methods, we illustrate two approaches to efficiency evaluation. The first approach is based on usage of real data, obtained through estimation of a set of model objects by a group of experts. The second approach is based on simulation of the whole expert examination cycle (including expert estimates). During evaluation of efficiency of the two listed modifications of combinatorial expert data aggregation method the simulation-based approach proved more robust and credible. Our experimental study confirms that if weights of spanning trees are taken into consideration, the results of combinatorial data aggregation method become more stable. So, weighted spanning tree enumeration method has an advantage over non-weighted method (and, consequently, over logarithmic least squares and row geometric mean methods).

cs.AI↗

arXiv2019

From Open Source Intelligence to Decision Making: a Hybrid Approach

We provide an overview of tools enabling users to utilize data from open sources for decision-making support in weakly-structured subject domains. Presently, it is impossible to replace expert data with data from open sources in the process of decision-making. Although organization of expert sessions requires much time and costs a lot, due to insufficient level of natural language processing technology development, we still have to engage experts and knowledge engineers in decision-making process. Information, obtained from experts and open sources, is processed, aggregated, and used as basis of recommendations, provided to decision-maker. As an example of a weakly-structured domain, we consider information conflicts and operations. For this domain we propose a hybrid decision support methodology, using data provided by both experts and open sources. The methodology is based on hierarchic decomposition of the main goal of an information operation. Using the data obtained from experts and open sources, we build the knowledge base of subject domain in the form of a weighted graph. It represents a hierarchy of factors influencing the main goal. Besides intensity, the impact of each factor is characterized by delay and duration. With these parameters taken into account, main goal achievement degree is calculated, and changes of target parameters of information operation object are monitored. In order to illustrate the suggested hybrid approach, we consider a real-life example, where we detect, monitor, and analyze actions intended to discredit the National academy of sciences of Ukraine. For this purpose, we use specialized decision-making support and content monitoring software.

cs.DB↗

arXiv2019

Usage of Decision Support Systems for Conflicts Modelling during Information Operations Recognition

Application of decision support systems for conflict modeling in information operations recognition is presented. An information operation is considered as a complex weakly structured system. The model of conflict between two subjects is proposed based on the second-order rank reflexive model. The method is described for construction of the design pattern for knowledge bases of decision support systems. In the talk, the methodology is proposed for using of decision support systems for modeling of conflicts in information operations recognition based on the use of expert knowledge and content monitoring.

cs.AI↗

arXiv2019

The (logarithmic) least squares optimality of the arithmetic (geometric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices

Complete and incomplete additive/multiplicative pairwise comparison matrices are applied in preference modelling, multi-attribute decision making and ranking. The equivalence of two well known methods is proved in this paper. The arithmetic (geometric) mean of weight vectors, calculated from all spanning trees, is proved to be optimal to the (logarithmic) least squares problem, not only for complete, as it was recently shown in Lundy, M., Siraj, S., Greco, S. (2017): The mathematical equivalence of the "spanning tree" and row geometric mean preference vectors and its implications for preference analysis, European Journal of Operational Research 257(1) 197-208, but for incomplete matrices as well. Unlike the complete case, where an explicit formula, namely the row arithmetic/geometric mean of matrix elements, exists for the (logarithmic) least squares problem, the incomplete case requires a completely different and new proof. Finally, Kirchhoff's laws for the calculation of potentials in electric circuits is connected to our results.

math.OC↗

arXiv2017

A Method with Feedback for Aggregation of Group Incomplete Pair-Wise Comparisons

A method for aggregation of expert estimates in small groups is proposed. The method is based on combinatorial approach to decomposition of pair-wise comparison matrices and to processing of expert data. It also uses the basic principles of Analytic Hierarchy/Network Process approaches, such as building of criteria hierarchy to decompose and describe the problem, and evaluation of objects by means of pair-wise comparisons. It allows to derive priorities based on group incomplete pair-wise comparisons and to organize feedback with experts in order to achieve sufficient agreement of their estimates. Double entropy inter-rater index is suggested for usage as agreement measure. Every expert is given an opportunity to use the scale, in which the degree of detail (number of points/grades) most adequately reflects this expert's competence in the issue under consideration, for every single pair comparison. The method takes all conceptual levels of individual expert competence (subject domain, specific problem, individual pair-wise comparison matrix, separate pair-wise comparison) into consideration. The method is intended to be used in the process of strategic planning in weakly-structured subject domains.

math.OC↗