IDEAS home Printed from https://ideas.repec.org/a/wsi/ijitdm/v14y2015i06ns0219622014500412.html
   My bibliography  Save this article

Double Helix Value Functions, Ordinal/Cardinal Approach, Additive Utility Functions, Multiple Criteria, Decision Paradigm, Process, and Types (Z Theory I)

Author

Listed:
  • Behnam Malakooti

    (Systems Engineering, Electrical Engineering and Computer Science Department, Case Western Reserve University, Cleveland, Ohio 44106, USA)

Abstract

Z Utility Theory refers to a class of nonlinear utility functions for solving Risk and Multiple Criteria Decision-Making problems. Z utility functions are hybrids of additive and nonadditive (nonlinear) functions. This paper addresses the concepts and assessment methods for the additive part of Z-utility functions for multiple criteria problems that satisfy the efficiency (nondominancy) principle. We provide a decision paradigm and guidelines on how to approach, formulate, and solve decision-making problems. We, also, overview the modeling of decision process based on four types of decision-making styles. For multi-criteria problems, a new definition of convex efficiency is introduced. Also polyhedral efficiency is developed for presenting multi-criteria efficiency (nondominancy) graphically. New double helix quasi-linear value functions for multi-criteria are developed. Two types of double helix value functions for solving bi-criteria (Advantages versus Disadvantages) and also risk problems are introduced: Food–Fun curves for expected values and Fight-Flight curves for expected risk values. Ordinal/Cardinal Approach (OCA) for assessment of additive utility functions is developed. Simple consistency tests to determine whether the assessed utility function satisfies ordinal and/or cardinal properties are provided. We show that OCA can also be used to solve outranking problems. We provide a critique of Analytic Hierarchy Process (AHP) for assessing additive value functions and show that the developed Ordinal/Cardinal Approach overcomes the shortcomings of AHP. We also develop a unified/integrated approach for simultaneous assessment of nonlinear value and additive (multi-criteria) utility functions. These results in an additive utility function that can be concave, convex, or hybrid concave/convex based on the nonlinear value function. Finally, we show an interactive paired comparisons approach for solving nonadditive and nonlinear utility functions for bi-criteria decision-making problems. Several illustrative examples are provided. The paper provides reliable and robust approaches for modeling the utility preferences of heterogeneous economic agents in macro and micro-economics.

Suggested Citation

  • Behnam Malakooti, 2015. "Double Helix Value Functions, Ordinal/Cardinal Approach, Additive Utility Functions, Multiple Criteria, Decision Paradigm, Process, and Types (Z Theory I)," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 1353-1400, November.
    • Handle: RePEc:wsi:ijitdm:v:14:y:2015:i:06:n:s0219622014500412
    DOI: 10.1142/S0219622014500412
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219622014500412
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219622014500412?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. James S. Dyer, 1990. "Remarks on the Analytic Hierarchy Process," Management Science, INFORMS, vol. 36(3), pages 249-258, March.
    2. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    3. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    4. Thomas L. Saaty, 1990. "An Exposition of the AHP in Reply to the Paper "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 259-268, March.
    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. A. M. Geoffrion & J. S. Dyer & A. Feinberg, 1972. "An Interactive Approach for Multi-Criterion Optimization, with an Application to the Operation of an Academic Department," Management Science, INFORMS, vol. 19(4-Part-1), pages 357-368, December.
    7. Keeney,Ralph L. & Raiffa,Howard, 1993. "Decisions with Multiple Objectives," Cambridge Books, Cambridge University Press, number 9780521438834, September.
    8. Stewart, Theodor J., 1999. "Evaluation and refinement of aspiration-based methods in MCDM," European Journal of Operational Research, Elsevier, vol. 113(3), pages 643-652, March.
    9. Ralph L. Keeney, 1974. "Multiplicative Utility Functions," Operations Research, INFORMS, vol. 22(1), pages 22-34, February.
    10. Maria Angelica Velazquez & David Claudio & A. Ravi Ravindran, 2010. "Experiments in multiple criteria selection problems with multiple decision makers," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 7(4), pages 413-428.
    11. James S. Dyer, 1990. "A Clarification of "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 274-275, March.
    12. Ballestero, Enrique, 2007. "Compromise programming: A utility-based linear-quadratic composite metric from the trade-off between achievement and balanced (non-corner) solutions," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1369-1382, November.
    13. Corner, J. L. & Buchanan, J. T., 1997. "Capturing decision maker preference: Experimental comparison of decision analysis and MCDM techniques," European Journal of Operational Research, Elsevier, vol. 98(1), pages 85-97, April.
    14. 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.
    15. Jonathan Ingersoll, 2008. "Non‐Monotonicity of the Tversky‐Kahneman Probability‐Weighting Function: A Cautionary Note," European Financial Management, European Financial Management Association, vol. 14(3), pages 385-390, June.
    16. Jyrki Wallenius & James S. Dyer & Peter C. Fishburn & Ralph E. Steuer & Stanley Zionts & Kalyanmoy Deb, 2008. "Multiple Criteria Decision Making, Multiattribute Utility Theory: Recent Accomplishments and What Lies Ahead," Management Science, INFORMS, vol. 54(7), pages 1336-1349, July.
    17. Tangian, Andranik, 2004. "A model for ordinally constructing additive objective functions," European Journal of Operational Research, Elsevier, vol. 159(2), pages 476-512, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ishizaka, Alessio & Siraj, Sajid, 2018. "Are multi-criteria decision-making tools useful? An experimental comparative study of three methods," European Journal of Operational Research, Elsevier, vol. 264(2), pages 462-471.
    2. Rodrigues, Teresa C. & Montibeller, Gilberto & Oliveira, Mónica D. & Bana e Costa, Carlos A., 2017. "Modelling multicriteria value interactions with Reasoning Maps," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1054-1071.
    3. Schneider, Frank, 2008. "Multiple criteria decision making in application layer networks," Bayreuth Reports on Information Systems Management 36, University of Bayreuth, Chair of Information Systems Management.
    4. Michele Bernasconi & Christine Choirat & Raffaello Seri, 2010. "The Analytic Hierarchy Process and the Theory of Measurement," Management Science, INFORMS, vol. 56(4), pages 699-711, April.
    5. Nikolaos Argyris & Alec Morton & José Rui Figueira, 2014. "CUT: A Multicriteria Approach for Concavifiable Preferences," Operations Research, INFORMS, vol. 62(3), pages 633-642, June.
    6. Katie Steele & Yohay Carmel & Jean Cross & Chris Wilcox, 2009. "Uses and Misuses of Multicriteria Decision Analysis (MCDA) in Environmental Decision Making," Risk Analysis, John Wiley & Sons, vol. 29(1), pages 26-33, January.
    7. Fowler, John W. & Gel, Esma S. & Köksalan, Murat M. & Korhonen, Pekka & Marquis, Jon L. & Wallenius, Jyrki, 2010. "Interactive evolutionary multi-objective optimization for quasi-concave preference functions," European Journal of Operational Research, Elsevier, vol. 206(2), pages 417-425, October.
    8. Bana e Costa, Carlos A. & Vansnick, Jean-Claude, 2008. "A critical analysis of the eigenvalue method used to derive priorities in AHP," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1422-1428, June.
    9. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, vol. 50(5), pages 561-574, May.
    10. Thomas L. Saaty, 2013. "The Modern Science of Multicriteria Decision Making and Its Practical Applications: The AHP/ANP Approach," Operations Research, INFORMS, vol. 61(5), pages 1101-1118, October.
    11. Madjid Tavana & Mariya Sodenkamp & Leena Suhl, 2010. "A soft multi-criteria decision analysis model with application to the European Union enlargement," Annals of Operations Research, Springer, vol. 181(1), pages 393-421, December.
    12. Nowak, Maciej, 2007. "Aspiration level approach in stochastic MCDM problems," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1626-1640, March.
    13. Yael Grushka-Cockayne & Bert De Reyck & Zeger Degraeve, 2008. "An Integrated Decision-Making Approach for Improving European Air Traffic Management," Management Science, INFORMS, vol. 54(8), pages 1395-1409, August.
    14. Katie Steele, 2009. "Response," Risk Analysis, John Wiley & Sons, vol. 29(11), pages 1494-1494, November.
    15. James G. Dolan & Donald R. Bordley, 1994. "Isoniazid Prophylaxis," Medical Decision Making, , vol. 14(1), pages 1-8, February.
    16. Zahir, Sajjad, 1999. "Geometry of decision making and the vector space formulation of the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 112(2), pages 373-396, January.
    17. Höfer, Tim & Sunak, Yasin & Siddique, Hafiz & Madlener, Reinhard, 2016. "Wind farm siting using a spatial Analytic Hierarchy Process approach: A case study of the Städteregion Aachen," Applied Energy, Elsevier, vol. 163(C), pages 222-243.
    18. Faramondi, Luca & Oliva, Gabriele & Setola, Roberto & Bozóki, Sándor, 2023. "Robustness to rank reversal in pairwise comparison matrices based on uncertainty bounds," European Journal of Operational Research, Elsevier, vol. 304(2), pages 676-688.
    19. Leung, Lawrence C. & Cao, Dong, 2001. "On the efficacy of modeling multi-attribute decision problems using AHP and Sinarchy," European Journal of Operational Research, Elsevier, vol. 132(1), pages 39-49, July.
    20. Jason R. W. Merrick & John R. Harrald, 2007. "Making Decisions About Safety in US Ports and Waterways," Interfaces, INFORMS, vol. 37(3), pages 240-252, June.

    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:wsi:ijitdm:v:14:y:2015:i:06:n:s0219622014500412. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijitdm/ijitdm.shtml .

    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.