Related papers: Inconsistency thresholds for incomplete pairwise c…
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…
Processing information, acquired by subjective assessments, involves inconsistency analysis in most (if not all) applications of which some are of considerable importance at a national level (see, Koczkodaj/Kulakowski/Ligenza,…
Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a…
Matrix regularity is a key to various problems in applied mathematics. The sufficient conditions, used for checking regularity of interval parametric matrices, usually fail in case of large parameter intervals. We present necessary and…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
In this work, we investigate the incompatibility of random quantum measurements. Most previous work has focused on characterizing the maximal amount of white noise that any fixed number of incompatible measurements with a fixed number of…
This paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum eigenvalue of the matrix sum is controlled by the minimum…
This paper studies decision-making and statistical inference for two-sided matching markets via matrix completion. In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise…
Pairwise comparison matrix as a crucial component of AHP, presents the prefer- ence relations among alternatives. However, in many cases, the pairwise comparison matrix is difficult to complete, which obstructs the subsequent operations of…
We analyze the structure of the disagreement among a population of voters over a set of alternatives. Surveys typically ask either for pairwise comparisons, simple and intuitive for participants, or full rankings over alternatives,…
This paper proposes an analysis of the effects of consensus and preference aggregation on the consistency of pairwise comparisons. We define some boundary properties for the inconsistency of group preferences and investigate their relation…
This paper shows how to manage null entries in pairwise comparisons matrices. Although assessments can be imprecise, since subjective criteria are involved, the classical pairwise comparisons theory expects all of them to be available. In…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
We consider fits to two or more datasets for which results from the sa me experiment share a common systematic uncertainty in addition to their individ ual statistical errors. This is important in extracting the maximum information from a…
The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
Statistical inference using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this paper, we propose a general framework to model the mutual interactions in a network, which enjoys ample…
We consider statistical procedures for hypothesis testing of real valued functionals of matched pairs with missing values. In order to improve the accuracy of existing methods, we propose a novel multiplication combination procedure.…
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…