Related papers: Notes on the existence of solutions in the pairwis…
The Heuristic Ratio Estimation (HRE) approach proposes a new way of using the pairwise comparisons matrix. It allows the assumption that the weights of some alternatives (herein referred to as concepts) are known and fixed, hence the weight…
Heuristic Rating Estimation (HRE) is a newly proposed method supporting decisions analysis based on the use of pairwise comparisons. It allows that the ranking values of some alternatives (herein referred to as concepts) are initially…
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…
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…
We examine three methods for ranking by pairwise comparison: Principal Eigenvector, HodgeRank and Tropical Eigenvector. It is shown that the choice of method can produce arbitrarily different rank order.To be precise, for any two of the…
An overview of current debates and contemporary research devoted to the modeling of decision making processes and their facilitation directs attention to the Analytic Hierarchy Process (AHP). At the core of the AHP are various…
The pairwise comparisons method is a convenient tool used when the relative order among different concepts (alternatives) needs to be determined. One popular implementation of the method is based on solving an eigenvalue problem for the…
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)…
Large Language Models (LLMs) have demonstrated promising capabilities as automatic evaluators in assessing the quality of generated natural language. However, LLMs still exhibit biases in evaluation and often struggle to generate coherent…
The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another taking into account all the instances of the assumed preference model…
We attack the problem of getting a strict ranking (i.e. a ranking without equally ranked items) of $n$ items from a pairwise comparisons matrix. Basic structures are described, a first heuristical approach based on a condition, the…
Recommender systems are one of the most pervasive applications of machine learning in industry, with many services using them to match users to products or information. As such it is important to ask: what are the possible fairness risks,…
There are many priority deriving methods for pairwise comparison matrices. It is known that when these matrices are consistent all these methods result in the same priority vector. However, when they are inconsistent, the results may vary.…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
Comparative Judgement is an assessment method where item ratings are estimated based on rankings of subsets of the items. These rankings are typically pairwise, with ratings taken to be the estimated parameters from fitting a Bradley-Terry…
Maximum likelihood estimation (MLE) and heuristic predictive estimation (HPE) are two widely used approaches in industrial uncertainty analysis. We review them from the point of view of decision theory, using Bayesian inference as a gold…
The pairwise comparisons method is a convenient tool used when the relative order of preferences among different concepts (alternatives) needs to be determined. There are several popular implementations of this method, including the…
Discovering relevant patterns for a particular user remains a challenging tasks in data mining. Several approaches have been proposed to learn user-specific pattern ranking functions. These approaches generalize well, but at the expense of…
Subjective assessment tests are often employed to evaluate image processing systems, notably image and video compression, super-resolution among others and have been used as an indisputable way to provide evidence of the performance of an…
We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to…