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Jiri Mazurek

Publications and source records attributed to Jiri Mazurek.

11 recordsLinked to original sources
arXiv2026

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.

cs.AI↗
arXiv2026

Mean-based incomplete pairwise comparisons method with the reference values

In this article, we propose two quantitative methods for calculating weight vectors for incomplete pairwise comparison matrices using reference values. Both procedures are extensions of arithmetic and geometric heuristic estimation (HRE) methods. The proposed solutions allow flexible selection of the number of reference alternatives and the range of comparisons, from the acceptable minimum to a complete set. In this paper, we prove that the newly introduced geometric HRE method for incomplete data is optimal. For this method, we also prove the existence of a feasible solution. In the paper, we also provide sufficient conditions for the existence of a solution for the second arithmetic variant of the HRE method. We illustrate the presented methods with numerical examples.

cs.AI↗
arXiv2026

On Intensity of Preference Rank Reversal in the AHP

The analytic hierarchy process (AHP) is one of the most widely used multicriteria decision-making methods, with applications from agriculture to space engineering. Despite its popularity, AHP has been repeatedly criticised for rank reversal, a phenomenon in which the ranking of alternatives changes after the addition or removal of an irrelevant or duplicate alternative. This paper introduces a new type of rank reversal in AHP, arising when the intensity of preferences is uniformly increased. We show that even when all pairwise preferences preserve their direction and are intensified identically, the eigenvector method may produce a different ordering of alternatives. In contrast, the geometric mean (GM) method is robust to this intensity-of-preference (IOP) rank reversal. The applicability of this result is shown through a real decision-making problem taken from a NASA manual concerning capability prioritisation for the planned lunar Gateway orbital station.

math.OC↗
arXiv2024

Establishing a leader in a pairwise comparisons method

Abstract Like electoral systems, decision-making methods are also vulnerable to manipulation by decision-makers. The ability to effectively defend against such threats can only come from thoroughly understanding the manipulation mechanisms. In the presented article, we show two algorithms that can be used to launch a manipulation attack. They allow for equating the weights of two selected alternatives in the pairwise comparison method and, consequently, choosing a leader. The theoretical considerations are accompanied by a Monte Carlo simulation showing the relationship between the size of the PC matrix, the degree of inconsistency, and the ease of manipulation. This work is a continuation of our previous research published in the paper (Szybowski et al., 2023)

cs.AI↗
arXiv2023

On the Derivation of Weights from Incomplete Pairwise Comparisons Matrices via Spanning Trees with Crisp and Fuzzy Confidence Levels

In this paper, we propose a new method for the derivation of a priority vector from an incomplete pairwise comparisons (PC) matrix. We assume that each entry of a PC matrix provided by an expert is also evaluated in terms of the expert's confidence in a particular judgment. Then, from corresponding graph representations of a given PC matrix, all spanning trees are found. For each spanning tree, a unique priority vector is obtained with the weight corresponding to the confidence levels of entries that constitute this tree. At the end, the final priority vector is obtained through an aggregation of priority vectors achieved from all spanning trees. Confidence levels are modeled by real (crisp) numbers and triangular fuzzy numbers. Numerical examples and comparisons with other methods are also provided. Last, but not least, we introduce a new formula for an upper bound of the number of spanning trees, so that a decision maker gains knowledge (in advance) on how computationally demanding the proposed method is for a given PC matrix.

math.OC↗
arXiv2023

Towards secure judgments aggregation in AHP

In decision-making methods, it is common to assume that the experts are honest and professional. However, this is not the case when one or more experts in the group decision making framework, such as the group analytic hierarchy process (GAHP), try to manipulate results in their favor. The aim of this paper is to introduce two heuristics in the GAHP, setting allowing to detect the manipulators and minimize their effect on the group consensus by diminishing their weights. The first heuristic is based on the assumption that manipulators will provide judgments which can be considered outliers with respect to those of the rest of the experts in the group. The second heuristic assumes that dishonest judgments are less consistent than the average consistency of the group. Both approaches are illustrated with numerical examples and simulations.

cs.AI↗
arXiv2019

Satisfaction of the Condition of Order Preservation: A Simulation Study

We examine satisfaction of the condition of order preservation (COP) with respect to different levels of inconsistency for randomly generated multiplicative pairwise comparison matrices (MPCMs) of the order n = {3,4,...,9}, where a priority vector is derived both by the eigenvalue method (EV) and the geometric mean (GM) method. Our results suggest the GM method and the EV method preserve the COP condition almost identically, both for the less inconsistent matrices (with Saaty's consistency index CI <0.10), and the more inconsistent matrices (with CI >= 0.10). Further, we find that the frequency of the COP violations grows (almost linearly) with increasing inconsistency of MPCMs measured by Koczkodaj's inconsistency index and Saaty's consistency index respectively, and we provide graphs to illustrate these relationships for MPCMs of the order n ={4, 7, 9}.

cs.DM↗
arXiv2018

When is the condition of order preservation met?

This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a generalization of previous results. Sufficient conditions for order preservation based on the properties of elements of pairwise comparisons matrix are derived. A numerical example is presented.

cs.DM↗
arXiv2018

Which Football Player Bears Most Resemblance to Messi? A Statistical Analysis

Many pundits and fans ask themselves the same question: Which football player bears most resemblance to Lionel Messi? Is it Chelsea's Eden Hazard? Is it Paulo Dybala, the heir to Messi in the national team of Argentina? Or is the most alike player to Messi someone completely else? In general, the research on the evaluation of players' performances originated in the context of baseball in the USA, but, currently, it is of great importance in almost every team sport on the planet. Specifically, football clubs' managers can use the data on player's similarity when looking for replacement of their players by other, presumably similar ones. Also, the research in the presented direction is certainly interesting both for football pundits and football fans. Therefore, the aim of this study is to answer the question from the title with the use of the statistical analysis based on the data from ongoing league season retrieved from WhoScored (WS) database. WS provides detailed data (up to 24 parameters such as goals scored, the number of assists, shots on goal, passes, dribbles or fouls) for players of TOP 5 European leagues, and ranks them with respect to their overall performance. For this study, 17 parameters (criteria) most relevant for an attacking player were used, and a set of 28 players, candidates to be 'most alike to Messi' from WS TOP 100 list were selected. After data normalization and application of a proper metric function the most similar player to Lionel Messi was found.

stat.OT↗
arXiv2017

On Inconsistency Indices and Inconsistency Axioms in Pairwise Comparisons

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several inconsistency indices were proposed as an alternative to Saaty inconsistency index and inconsistency ratio for reciprocal pairwise comparisons matrices. This paper aims to: firstly, introduce a new measure of inconsistency of pairwise comparisons and to prove its basic properties; secondly, to postulate an additional axiom, an upper boundary axiom, to an existing set of axioms; and the last, but not least, the paper provides proofs of satisfaction of this additional axiom by selected inconsistency indices as well as it provides their numerical comparison.

cs.AI↗