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The use of quasi-concave value functions in MCDM: some theoretical results

Author

Listed:
  • Pekka Korhonen

    (Aalto University)

  • Majid Soleimani-damaneh

    (University of Tehran
    Institute for Research in Fundamental Sciences (IPM))

  • Jyrki Wallenius

    (Aalto University)

Abstract

In this paper we answer three important questions about the convex-cone dominance approach in Multiple Criteria Decision Making with a finite number of alternatives. These questions concern the existence of value (utility) functions and the consistency of the preference information with special forms of this function.

Suggested Citation

  • Pekka Korhonen & Majid Soleimani-damaneh & Jyrki Wallenius, 2017. "The use of quasi-concave value functions in MCDM: some theoretical results," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 367-375, October.
    • Handle: RePEc:spr:mathme:v:86:y:2017:i:2:d:10.1007_s00186-017-0601-5
    DOI: 10.1007/s00186-017-0601-5
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    References listed on IDEAS

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    1. Korhonen, Pekka & Soleimani-damaneh, Majid & Wallenius, Jyrki, 2016. "Dual cone approach to convex-cone dominance in multiple criteria decision making," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1139-1143.
    2. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    3. Srinivas Y. Prasad & Mark H. Karwan & Stanley Zionts, 1997. "Use of Convex Cones in Interactive Multiple Objective Decision Making," Management Science, INFORMS, vol. 43(5), pages 723-734, May.
    4. Stanley Zionts & Jyrki Wallenius, 1976. "An Interactive Programming Method for Solving the Multiple Criteria Problem," Management Science, INFORMS, vol. 22(6), pages 652-663, February.
    5. Pekka Korhonen & Jyrki Wallenius & Stanley Zionts, 1984. "Solving the Discrete Multiple Criteria Problem using Convex Cones," Management Science, INFORMS, vol. 30(11), pages 1336-1345, November.
    6. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
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    Cited by:

    1. Peter Reichert & Klemens Niederberger & Peter Rey & Urs Helg & Susanne Haertel-Borer, 2019. "The need for unconventional value aggregation techniques: experiences from eliciting stakeholder preferences in environmental management," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 197-219, November.
    2. Soleimani-damaneh, Majid & Pourkarimi, Latif & Korhonen, Pekka J. & Wallenius, Jyrki, 2021. "An operational test for the existence of a consistent increasing quasi-concave value function," European Journal of Operational Research, Elsevier, vol. 289(1), pages 232-239.
    3. Nasim Nasrabadi & Akram Dehnokhalaji & Pekka Korhonen & Jyrki Wallenius, 2019. "Using convex preference cones in multiple criteria decision making and related fields," Journal of Business Economics, Springer, vol. 89(6), pages 699-717, August.

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