Related papers: New inconsistency indicators for incomplete pairwi…
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,…
We introduce several novel change of measure inequalities for two families of divergences: $f$-divergences and $\alpha$-divergences. We show how the variational representation for $f$-divergences leads to novel change of measure…
This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into…
A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…
We examine the notion of inconsistency in pairwise comparisons and propose an axiomatization which is independent of any method of approximation or the inconsistency indicator definition (e.g., Analytic Hierarchy Process, AHP). It has been…
We investigate an application of a mathematically robust minimization method -- the gradient method -- to the consistencization problem of a pairwise comparisons (PC) matrix. Our approach sheds new light on the notion of a priority vector…
Mathematical analysis of the analytic hierarchy process (AHP) led to the development of a mathematical function, usually called the inconsistency index, which has the center role in measuring the inconsistency of the judgements in AHP.…
To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original…
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided.…
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
Towards a solution to the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of 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)…
We provide an analysis of complementarity via a suitably designed classicalmodel that leads to a set of inequalities that can be tested by means ofunsharp measurements. We show that, if the measured statistics does notfulfill the…
Comparing alternatives in pairs is a well-known method of ranking creation. Experts are asked to perform a series of binary comparisons and then, using mathematical methods, the final ranking is prepared. As experts conduct the individual…
We investigate the problem of inconsistency measurement on large knowledge bases by considering stream-based inconsistency measurement, i.e., we investigate inconsistency measures that cannot consider a knowledge base as a whole but process…
How should we quantify the inconsistency of a database that violates integrity constraints? Proper measures are important for various tasks, such as progress indication and action prioritization in cleaning systems, and reliability…
Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually…
We investigate the application of inconsistency measures to the problem of analysing business rule bases. Due to some intricacies of the domain of business rule bases, a straightforward application is not feasible. We therefore develop some…
We study some new invariant measures arising from local inverse iterates. Examples are also given.
Measures of discordance between datasets have become an essential part of cosmological analyses. It is important to accurately evaluate the significance of such discordances when present. We propose here a Bayesian interpretation of…