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Comparison of linear interpolation and arctan approximation of one-dimensional monotonic utility functions based on experimental data
Citation
Nikolova, N and Tenekedjiev, K and Dong, F and Hirota, K, Comparison of linear interpolation and arctan approximation of one-dimensional monotonic utility functions based on experimental data, Control and Cybernetics, 38, (3) pp. 835-861. ISSN 0324-8569 (2009) [Refereed Article]
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Abstract
Elicitation of utilities is among the most time consuming
tasks in decision analysis. We search for ways to shorten
this phase without compromising the quality of results. We use the
results from an empirical experiment with 104 participants. They
elicited 9 inner nodes from their one-dimensional utility function
over monetary gains and losses using three elicitation techniques.
A specific feature of the results is their interval character, as the
elicitators are fuzzy rational individuals. The data is used to construct
arctan-approximated and linearly interpolated utilities and
to compare the results. We form partial samples with 3, 4 and 5
nodes for each participant and each elicitation method, and again
interpolate/approximate the utilities. We introduce goodness-of-fit
and deterioration measures to analyze the decrease in quality of
the utility function due to reduced data nodes. The analysis, using
paired-sample tests, leads to the following conclusions: 1) arctanapproximation
is more adequate than linear interpolation over the
whole samples; 2) 5 inner nodes are sufficient to construct a satisfactory
arctan-approximation; 3) arctan-approximation and linear
interpolation are almost equal in quality over the partial samples,
but the local risk aversion of the linearly interpolated utility function
is of poor quality unlike that of the arctan-approximated utility
function.
Item Details
| Item Type: | Refereed Article |
|---|---|
| Keywords: | utility function, interpolation |
| Research Division: | Information and Computing Sciences |
| Research Group: | Information Systems |
| Research Field: | Decision Support and Group Support Systems |
| Objective Division: | Expanding Knowledge |
| Objective Group: | Expanding Knowledge |
| Objective Field: | Expanding Knowledge in the Information and Computing Sciences |
| UTAS Author: | Nikolova, N (Professor Nataliya Nikolova) |
| UTAS Author: | Tenekedjiev, K (Professor Kiril Tenekedjiev) |
| ID Code: | 127966 |
| Year Published: | 2009 |
| Web of Science® Times Cited: | 1 |
| Deposited By: | AMC Governance Office |
| Deposited On: | 2018-08-26 |
| Last Modified: | 2018-09-10 |
| Downloads: | 0 |
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