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A method based on the ideal and nadir solutions for stochastic MADM problems

Author

Listed:
  • Yan-Ping Jiang
  • Hai-Ming Liang
  • Minghe Sun

    (UTSA)

Abstract
Many real life decision making problems can be modeled as stochastic multi-attribute decision making (MADM) problems. A novel method for stochastic MADM problems is developed based on the ideal and nadir solutions as in the classical TOPSIS method. In a stochastic MADM problem, the evaluations of the alternatives with respect to the different attributes are represented by discrete stochastic variables. According to stochastic dominance rules, the probability distributions of the ideal and nadir variates, both are discrete stochastic variables, are defined and determined for a set of stochastic variables. A metric is proposed to measure the distance between two discrete stochastic variables. The ideal solution is a vector of ideal variates and the nadir solution is vector of nadir variates for the multiple attributes. As in the classical TOPSIS method, the relative closeness of an alternative is determined by its distances from the ideal and nadir solutions. The rankings of the alternatives are determined using the relative closeness. Examples are presented to illustrate the effectiveness of the proposed method. Through the examples, several significant advantages of the proposed method over some existing methods are discussed.

Suggested Citation

  • Yan-Ping Jiang & Hai-Ming Liang & Minghe Sun, 2014. "A method based on the ideal and nadir solutions for stochastic MADM problems," Working Papers 0178mss, College of Business, University of Texas at San Antonio.
    • Handle: RePEc:tsa:wpaper:0178mss
    as

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    File URL: http://interim.business.utsa.edu/wps/mss/0012MSS-061-2014.pdf
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    References listed on IDEAS

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    1. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    2. Lahdelma, Risto & Salminen, Pekka, 2009. "Prospect theory and stochastic multicriteria acceptability analysis (SMAA)," Omega, Elsevier, vol. 37(5), pages 961-971, 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. Martel, Jean-Marc & D'Avignon, Gilles R. & Couillard, Jean, 1986. "A fuzzy outranking relation in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 25(2), pages 258-271, May.
    5. Nowak, Maciej, 2004. "Preference and veto thresholds in multicriteria analysis based on stochastic dominance," European Journal of Operational Research, Elsevier, vol. 158(2), pages 339-350, October.
    6. Zaras, Kazimierz, 2001. "Rough approximation of a preference relation by a multi-attribute stochastic dominance for determinist and stochastic evaluation problems," European Journal of Operational Research, Elsevier, vol. 130(2), pages 305-314, April.
    7. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
    8. Martel, Jean M. & d'Avignon, Gilles R., 1982. "Projects ordering with multicriteria analysis," European Journal of Operational Research, Elsevier, vol. 10(1), pages 56-69, May.
    9. Theodor J Stewart, 2005. "Dealing with Uncertainties in MCDA," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 445-466, Springer.
    10. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    11. Zaras, Kazimierz, 2004. "Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems," European Journal of Operational Research, Elsevier, vol. 159(1), pages 196-206, November.
    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. D'Avignon, G. R. & Vincke, Ph., 1988. "An outranking method under uncertainty," European Journal of Operational Research, Elsevier, vol. 36(3), pages 311-321, September.
    14. Fan, Zhi-Ping & Ma, Jian & Jiang, Yan-Ping & Sun, Yong-Hong & Ma, Louis, 2006. "A goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 174(1), pages 311-321, October.
    15. Fan, Zhi-Ping & Liu, Yang & Feng, Bo, 2010. "A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations," European Journal of Operational Research, Elsevier, vol. 207(2), pages 906-915, December.
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    More about this item

    Keywords

    stochastic MADM; TOPSIS; ranking; ideal and nadir solutions; relative closeness;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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