Pairwise comparison matrices and the error-free property of the decision maker

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal

Graph Refinement based Airway Extraction using Mean-Field Networks and Graph Neural Networks

Graph refinement, or the task of obtaining subgraphs of interest from over-complete graphs, can have many varied applications. In this work, we extract trees or collection of sub-trees from image data by, first deriving a graph-based representation of the volumetric data and then, posing the tree extraction as a graph refinement task. We present two methods to perform graph refinement. First, we use mean-field approximation (MFA) to approximate the posterior density over the subgraphs from which the optimal subgraph of interest can be estimated. Mean field networks (MFNs) are used for inference based on the interpretation that iterations of MFA can be seen as feed-forward operations in a neural network. This allows us to learn the model parameters using gradient descent. Second, we present a supervised learning approach using graph neural networks (GNNs) which can be seen as generalisations of MFNs. Subgraphs are obtained by training a GNN-based graph refinement model to directly predict edge probabilities. We discuss connections between the two classes of methods and compare them for the task of extracting airways from 3D, low-dose, chest CT data. We show that both the MFN and GNN models show significant improvement when compared to one baseline method, that is similar to a top performing method in the EXACT'09 Challenge, and a 3D U-Net based airway segmentation model, in detecting more branches with fewer false positives.Comment: Accepted for publication at Medical Image Analysis. 14 page

Consistency of the decision-maker in pair-wise comparisons

Most authors assume that the natural behaviour of the decision-maker is being inconsistent. This paper investigates the main sources of inconsistency and analyses methods for reducing or eliminating inconsistency. Decision support systems can contain interactive modules for that purpose. In a system with consistency control, there are three stages. First, consistency should be checked: a consistency measure is needed. Secondly, approval or rejection has to be decided: a threshold value of inconsistency measure is needed. Finally, if inconsistency is ‘high’, corrections have to be made: an inconsistency reducing method is needed. This paper reviews the difficulties in all stages. An entirely different approach is to elaborate a decision support system in order to force the decision-maker to give consistent values in each step of answering pair-wise comparison questions. An interactive questioning procedure resulting in consistent (sub) matrices has been demonstrated