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Researcher profile

Konrad Kułakowski

Konrad Kułakowski contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Discrete MathematicsArtificial Intelligenceecon.EMmath.STStatistics Theory

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Published work

4 published item(s)

preprint2026arXiv

Sufficient conditions for a Heuristic Rating Estimation Method application

A series of papers has introduced the Heuristic Rating Estimation method, which evaluates a set of alternatives based on pairwise comparisons and the weights of reference alternatives. We formulate the conditions under which the HRE method can be applied correctly. The research considers both arithmetic and geometric algorithms for complete and incomplete pairwise comparison methods. The illustrative examples show that the estimations of inconsistency in the arithmetic variant are optimal.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Multiple-criteria Heuristic Rating Estimation

One of the most widespread multi-criteria decision-making methods is the Analytic Hierarchy Process (AHP). AHP successfully combines the pairwise comparisons method and the hierarchical approach. It allows the decision-maker to set priorities for all ranked alternatives. But what if, for some of them, their ranking value is known (e.g., it can be determined differently)? The Heuristic Rating Estimation (HRE) method proposed in 2014 tried to bring the answer to this question. However, the considerations were limited to a model that did not consider many criteria. In this work, we go a step further and analyze how HRE can be used as part of the AHP hierarchical framework. The theoretical considerations are accompanied by illustrative examples showing HRE as a multiple-criteria decision-making method.

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preprint2022arXiv

Some Notes on the Similarity of Priority Vectors Derived by the Eigenvalue Method and the Geometric Mean Method

This paper examines the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. First, we introduce several propositions on the (dis)similarity of both rankings concerning the matrix size and its inconsistency expressed by the Koczkodaj's inconsistency index. Further on, we examine the relationship between differences in both rankings and Kendall's rank correlation coefficient $τ$ and Spearman's rank coefficient $ρ$. Apart from theoretical results, intuitive numerical examples and Monte Carlo simulations are also provided.

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preprint2019arXiv

Inconsistency indices for incomplete pairwise comparisons matrices

Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for determining the level of inconsistency among compared alternatives. Unfortunately, most of them assume that the set of comparisons is complete, i.e. every single alternative is compared to each other. This is not true and the ranking must sometimes be made based on incomplete data. In order to fill this gap, this work aims to adapt the selected twelve existing inconsistency indices for the purpose of analyzing incomplete data sets. The modified indices are subjected to Monte Carlo experiments. Those of them that achieved the best results in the experiments carried out are recommended for use in practice.

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