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Multiattribute Utility Functions: Decompositions Using Interpolation

Author

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  • David E. Bell

    (Harvard University)

Abstract

Methodologies developed in the last several years allow formal inclusion of two sources of complexity in the analysis of a decision problem--uncertainty and multiple conflicting objectives. Uncertainty can be handled by assessing the decision maker's attitude towards risk in the form of a von Neumann-Morgenstern utility function. Conflicting objectives may be handled by making the utility function multidimensional. A problem that then arises is in devising assessment protocols for these multidimensional (multiattribute) functions that make efficient use of the decision maker's time and effort. Mostly, such methods have concentrated on identifying structural properties of the function, such as separability, by asking questions of a general nature about the preferences and tradeoffs of the decision maker. These methods have been applied successfully on such problems as facilities siting, selection of appropriate medical treatment, optimal pest control and the evaluation of R&D proposals. The problem addressed in this paper is that of what to do about the assessment if no useful decomposition of the utility function can be identified. One possiblity is to make use of some of the properties that were most nearly satisfied and then attempt to support the resulting recommendations with a sensitivity analysis. This paper provides the analyst with an efficient, routine method of approximating the utility function to any degree of accuracy that the decision maker or the problem requires. The idea is to assess the function exactly only on a multidimensional grid and then to interpolate other values of the utility function from those on the grid. Evidently, a finer grid will, in general, provide a better approximation. The resulting utility function is continuous. It is not anticipated that many of the problems in which conflicting objectives are a factor will need this level of sophistication. But just as there are problems that require a substantial modelling effort to identify feasible consequences so, occasionally, an analysis would benefit from an accurate modelling of the objective function.

Suggested Citation

  • David E. Bell, 1979. "Multiattribute Utility Functions: Decompositions Using Interpolation," Management Science, INFORMS, vol. 25(8), pages 744-753, August.
  • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:8:p:744-753
    DOI: 10.1287/mnsc.25.8.744
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    Citations

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    Cited by:

    1. Corrente, Salvatore & Greco, Salvatore & Ishizaka, Alessio, 2016. "Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression," Omega, Elsevier, vol. 61(C), pages 2-18.
    2. Ali E. Abbas & Zhengwei Sun, 2019. "Archimedean Utility Copulas with Polynomial Generating Functions," Decision Analysis, INFORMS, vol. 16(3), pages 218-237, September.
    3. James S. Dyer & James E. Smith, 2021. "Innovations in the Science and Practice of Decision Analysis: The Role of Management Science," Management Science, INFORMS, vol. 67(9), pages 5364-5378, September.
    4. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    5. Ali E. Abbas & Zhengwei Sun, 2015. "Multiattribute Utility Functions Satisfying Mutual Preferential Independence," Operations Research, INFORMS, vol. 63(2), pages 378-393, April.
    6. Adam Safron, 2019. "Multilevel evolutionary developmental optimization (MEDO): A theoretical framework for understanding preferences and selection dynamics," Papers 1910.13443, arXiv.org, revised Nov 2019.
    7. Jiehua Xie & Zhengyong Zhou, 2022. "Patchwork Constructions of Multiattribute Utility Functions," Decision Analysis, INFORMS, vol. 19(2), pages 141-169, June.
    8. Ali E. Abbas & Ronald A. Howard, 2005. "Attribute Dominance Utility," Decision Analysis, INFORMS, vol. 2(4), pages 185-206, December.
    9. Ali E. Abbas, 2011. "The Multiattribute Utility Tree," Decision Analysis, INFORMS, vol. 8(3), pages 180-205, September.
    10. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, vol. 50(5), pages 561-574, May.
    11. Abdildin, Yerkin G. & Abbas, Ali E., 2016. "Analysis of decision alternatives of the deep borehole filter restoration problem," Energy, Elsevier, vol. 114(C), pages 1306-1321.
    12. Ali E. Abbas & David E. Bell, 2015. "Ordinal One-Switch Utility Functions," Operations Research, INFORMS, vol. 63(6), pages 1411-1419, December.
    13. Ali E. Abbas, 2013. "Utility Copula Functions Matching All Boundary Assessments," Operations Research, INFORMS, vol. 61(2), pages 359-371, April.

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