Related papers: Pairwise Comparisons Simplified

This paper examines the use of Lie group and Lie Algebra theory to construct the geometry of pairwise comparisons matrices. The Hadamard product (also known as coordinatewise, coordinate-wise, elementwise, or element-wise product) is…

We revisit simple and powerful methods for multiple pairwise comparisons that can be used in designs with three groups. We argue that the proper choice of method should be determined by the assessment which of the comparisons are considered…

This study demonstrates that incorrect data are entered into a pairwise comparisons matrix for processing into weights for the data collected by a rating scale. Unprocessed rating scale data lead to a paradox. A solution to it, based on…

A paired comparison analysis is the simplest way to make comparative judgments between objects where objects may be goods, services or skills. For a set of problems, this technique helps to choose the most important problem to solve first…

We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced…

When creating the ranking based on the pairwise comparisons very often, we face difficulties in completing all the results of direct comparisons. In this case, the solution is to use the ranking method based on the incomplete PC matrix. The…

This study proposes revised axioms for defining inconsistency indicators in pairwise comparisons. It is based on the new findings that "PC submatrix cannot have a worse inconsistency indicator than the PC matrix containing it" and that…

A simple recursive scheme for parameterisation of n-by-n unitary matrices is presented.

Pairwise comparison matrices are widely used in Multicriteria Decision Making. This article applies incomplete pairwise comparison matrices in the area of sport tournaments, namely proposing alternative rankings for the 2010 Chess Olympiad…

Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of…

We study very simple sorting algorithms based on a probabilistic comparator model. In our model, errors in comparing two elements are due to (1) the energy or effort put in the comparison and (2) the difference between the compared…

Dealing with large numbers of symmetries is often problematic. One solution is to focus on just symmetries that generate the symmetry group. Whilst there are special cases where breaking just the symmetries in a generating set is complete,…

This paper examines the constricted use of group theory in the studies of pairwise comparisons. The presented approach is based on the application of the famous Levi Theorems of 1942 and 1943 for orderable groups. The theoretical foundation…

Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the…

We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…

We present a novel framework for machine translation evaluation using neural networks in a pairwise setting, where the goal is to select the better translation from a pair of hypotheses, given the reference translation. In this framework,…

In this paper, we propose a machine learning model for sparse pairwise comparison matrices (PCMs), combining classical PCM approaches with graph-based learning techniques. Numerical results are provided to demonstrate the effectiveness and…

Several clustering methods (e.g., Normalized Cut and Ratio Cut) divide the Min Cut cost function by a cluster dependent factor (e.g., the size or the degree of the clusters), in order to yield a more balanced partitioning. We, instead,…

This paper describes the transition of a male-pessimal matching set to optimal when it is a man-oriented approach by deleting a pair from matching set considering the score based approach. A descriptive explanation of the proposed algorithm…

Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and…