IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v23y1975i5p941-967.html
   My bibliography  Save this article

A Fractional Hypercube Decomposition Theorem for Multiattribute Utility Functions

Author

Listed:
  • Peter H. Farquhar

    (Northwestern University, Evanston, Illinois)

Abstract

This paper establishes a fundamental decomposition theorem in multiattribute utility theory. The methodology uses fractional hypercubes to generate a variety of attribute independence conditions that are necessary and sufficient for various decompositions: the additive, Keeney's quasi-additive, Fishburrt's diagonal, and others. These other nonaddirive utility decompositions contain some nonseparable interaction terms and are therefore applicable to decision problems not covered by earlier models. The paper defines a fractional hypercube and introduces the corresponding multiple element conditional preference order. The main theorem is produced from the solution of equations that are derived from transformations of linear functions that preserve these conditional preference orders. The computations and scaling required in implementing the main result are demonstrated by obtaining four utility decompositions on three attributes: apex, diagonal, quasi-pyramid, and semicube. We illustrate the methodology with geometric structures that correspond to the fractional hypercubes.

Suggested Citation

  • Peter H. Farquhar, 1975. "A Fractional Hypercube Decomposition Theorem for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 23(5), pages 941-967, October.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:5:p:941-967
    DOI: 10.1287/opre.23.5.941
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.23.5.941
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.23.5.941?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.
    2. Jiehua Xie & Zhengyong Zhou, 2022. "Patchwork Constructions of Multiattribute Utility Functions," Decision Analysis, INFORMS, vol. 19(2), pages 141-169, June.
    3. 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.
    4. L. Robin Keller & Jay Simon, 2019. "Preference Functions for Spatial Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 39(1), pages 244-256, January.
    5. Ali E. Abbas & Ronald A. Howard, 2005. "Attribute Dominance Utility," Decision Analysis, INFORMS, vol. 2(4), pages 185-206, December.
    6. Ali E. Abbas & Zhengwei Sun, 2019. "Archimedean Utility Copulas with Polynomial Generating Functions," Decision Analysis, INFORMS, vol. 16(3), pages 218-237, September.
    7. Ali E. Abbas, 2011. "The Multiattribute Utility Tree," Decision Analysis, INFORMS, vol. 8(3), pages 180-205, September.
    8. Hauser, John R. & Urban, Glen L., 1975. "A normative methodology for modeling consumer response to innovation," Working papers 785-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    9. Han Bleichrodt & Ulrich Schmidt & Horst Zank, 2009. "Additive Utility in Prospect Theory," Management Science, INFORMS, vol. 55(5), pages 863-873, May.
    10. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    11. Ali E. Abbas & Zhengwei Sun, 2015. "Multiattribute Utility Functions Satisfying Mutual Preferential Independence," Operations Research, INFORMS, vol. 63(2), pages 378-393, April.
    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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:23:y:1975:i:5:p:941-967. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.