An extended minimax disparity to determine the OWA operator weights

This paper contributes to extend the minimax disparity to determine the ordered weighted averaging (OWA) model based on linear programming. It introduces the minimax disparity approach between any distinct pairs of the weights and uses the duality of linear programming to prove the feasibility of the extended OWA operator weights model. The paper finishes with an open problem. © 2006 Elsevier Ltd. All rights reserved.

Zero weights and non-zero slacks:different solution to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.

Determining more realistic OWA weights

The concept of ordered weighted averaging (OWA) operator weights arises in uncertain decision making problems, however some weights may have a specific relationship with other. This information about the weights can be obtained from decision makers (DMs). This paper intends to introduce a theory of weight restrictions into the existing OWA operator weight models. Based on the DMs' value judgment the obtained OWA operator weights could be more realistic.

Effect of disability glare on visual performance

The object of the study was to investigate, establish and quantify the relationship between contrast sensitivity, intraocular light scatter and glare. The aim was to establish the effects on vision, in an effort to provide a more comprehensive understanding of the visual world of subjects prone to increased light scatter in the eye. Disability glare refers to the reduction in visual performance produced by a glare source. The reduction in visual performance can be explained by intraocular scattered light producing a veiling luminance which is superimposed upon the retinal image. This veiling luminance lowers contrast thus sensitivity to the stimulus declines. The effect of glare of luminance and colour contrast sensitivity for young and elderly subjects was examined. For both age groups, disability glare was greatest for the red-green stimulus and least for the blue-yellow. The precise effect of a glare source on colour discrimination depends upon the interaction between the chromaticity of the glare source and that of the stimulus. The effect of a long wavelength pass (red) and a short wavelength pass filter (blue) on disability glare was examined. Disability glare was not significantly different with the red and blue filters, even in the presence of wavelength dependent scatter. An equation was derived which allowed an intrinsic Light Scatter Factor (LSF) to be determined for any given glare angle (Paulsson and Sjöstrand, 1980). Corrections to the formula to account for factors such as pupil size changes are unnecessary. The results confirm the suitability of measuring the LSF using contrast threshold with and without glare, provided that appropriate methods are used. Using this formula an investigation into the amount of wavelength dependent scatter indicated that wavelength dependent scatter in normal young, elderly or cataractous eyes is of little or no significance. Finally, it seemed desirable to investigate the effect ultraviolet (UV) radiation has on intraocular light scatter and subsequently visual performance. Overall the results indicated that the presence or absence of UV radiation has relatively little effect on visual function for the young, elderly or cataract patient.

A method for automatically eliciting node weights in a hierarchical knowledge-based structure for reasoning with uncertainty

Hierarchical knowledge structures are frequently used within clinical decision support systems as part of the model for generating intelligent advice. The nodes in the hierarchy inevitably have varying influence on the decisionmaking processes, which needs to be reflected by parameters. If the model has been elicited from human experts, it is not feasible to ask them to estimate the parameters because there will be so many in even moderately-sized structures. This paper describes how the parameters could be obtained from data instead, using only a small number of cases. The original method [1] is applied to a particular web-based clinical decision support system called GRiST, which uses its hierarchical knowledge to quantify the risks associated with mental-health problems. The knowledge was elicited from multidisciplinary mental-health practitioners but the tree has several thousand nodes, all requiring an estimation of their relative influence on the assessment process. The method described in the paper shows how they can be obtained from about 200 cases instead. It greatly reduces the experts’ elicitation tasks and has the potential for being generalised to similar knowledge-engineering domains where relative weightings of node siblings are part of the parameter space.