Management Science and Financial Engineering

The Korean Operations Research and Management Science Society (한국경영과학회)
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Dominance, Potential Optimality, and Strict Preference Information in Multiple Criteria Decision Making

  • Received : 2011.03.29
  • Accepted : 2011.06.10
  • Published : 2011.11.30
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Abstract

The ordinary multiple criteria decision making (MCDM) approach requires two types of input, alternative values and criterion weights, and employs two schemes of alternative prioritization, dominance and potential optimality. This paper allows for incomplete information on both types of input and gives rise to the dominance relationships and potential optimality of alternatives. Unlike the earlier studies, we emphasize that incomplete information frequently takes the form of strict inequalities, such as strict orders and strict bounds, rather than weak inequalities. Then the issues of rising importance include: (1) The standard mathematical programming approach to prioritize alternatives cannot be used directly, because the feasible region for the permissible decision parameters becomes an open set. (2) We show that the earlier methods replacing the strict inequalities with weak ones, by employing a small positive number or zeroes, which closes the feasible set, may cause a serious problem and yield unacceptable prioritization results. Therefore, we address these important issues and develop a useful and simple method, without selecting any small value for the strict preference information. Given strict information on both types of decision parameters, we first construct a nonlinear program, transform it into a linear programming equivalent, and finally solve it via a two-stage method. An application is also demonstrated herein.

Keywords

References

  1. Ahn, B. S., "Extending Malakooti's model for ranking multicriteria alternatives with preference strength and partial information," IEEE Trans. Syst., Man, Cybern., Part A 33 (2003), 281-287. https://doi.org/10.1109/TSMCA.2003.817049
  2. Anandalingam, G. and C. E. Olsson, "A multi-stage multi-attribute decision model for project selection," Eur. J. Opl. Res. 43 (1989), 271-283. https://doi.org/10.1016/0377-2217(89)90226-9
  3. Arnold, V. I., I. Bardhan, W. W. Cooper, and A. Gallegos, "Primal and dual optimality in computer codes using two-stage solution procedures in DEA," Operations Research: Methods, Models and Applications, Aranson, J. and S. Zionts, (Eds.), Quorum Books: Westport, CT, (1998), 57-96.
  4. Athanassopoulos, A. D. and V. V. Podinovski, "Dominance and potential optimality in multiple criteria decision analysis with imprecise information," J. Opl. Res. Soc. 48 (1997), 142-150. https://doi.org/10.1057/palgrave.jors.2600345
  5. Barron, F. H. and B. E. Barret, "Decision quality using ranked attribute weights," Mngt. Sci. 42 (1996), 1515-1523. https://doi.org/10.1287/mnsc.42.11.1515
  6. Belton, V. and S. P. Vickers, "Demystifying DEA-A visual interactive approach based on multiple criteria analysis," J. Opl. Res. Soc. 44 (1993), 883-896.
  7. Bouyssou, D., "Using DEA as a tool for MCDM: Some remarks," J. Opl. Res. Soc. 50 (1999), 974-978. https://doi.org/10.1057/palgrave.jors.2600800
  8. Cook, W. D., J. Doyle, R. Green, and M. Kress, "Multiple criteria modeling and ordinal data: Evaluation in terms of subsets of criteria," Eur. J. Opl. Res. 98 (1997), 602-609. https://doi.org/10.1016/S0377-2217(96)00069-0
  9. Cook, W. D. and M. Kress, "A multiple criteria decision model with ordinal preference data," Eur. J. Opl. Res. 54 (1991), 191-198. https://doi.org/10.1016/0377-2217(91)90297-9
  10. Cooper, W. W., L. M. Seiford, and K. Tone, Data Envelopment Analysis: A Comprehensive Text with Models, Applications, and References and DEA-Solver Software, Kluwer-Academic Publishers: Boston, 2000.
  11. Craig, C. S. and S. P. Douglas, International Marketing Research, John Wiley and Sons Ltd: New York, 2005.
  12. Daniels, J. D., L. H. Radebaugh, and D. P. Sullivan, International Business: Environments and Operations, Prentice Hall: Upper Saddle River, New Jersey, 2008.
  13. Dyer, J. S. and R. K. Sarin, "Measurable multiattribute value functions," Opns. Res. 27 (1979), 810-822. https://doi.org/10.1287/opre.27.4.810
  14. Fishburn, P. C., "Analysis of decisions with incomplete knowledge of probabilities," Opns. Res. 13 (1965), 217-237. https://doi.org/10.1287/opre.13.2.217
  15. Hazen, G. B., "Partial information, dominance, and potential optimality in multiattribute utility theory," Opns. Res. 34 (1986), 296-310. https://doi.org/10.1287/opre.34.2.296
  16. Jimenez, A., S. Rios-Insua, and A. Mateos, "A generic multi-attribute analysis system," Comp. and Opns. Res. 33 (2006), 1081-1101. https://doi.org/10.1016/j.cor.2004.09.003
  17. Keeney, R. L. and H. Raiffa, Decisions with Multiple Objectives: Preferences and Value Tradeoffs, Wiley: New York, 1976.
  18. Kirkwood, C. W. and J. L. Corner, "The effectiveness of partial information about attribute weights for ranking alternatives in multiattribute decision making," Org. Behavior and Human Dec. Pro. 54 (1993), 456-476. https://doi.org/10.1006/obhd.1993.1019
  19. Kirkwood, C. W. and R. K. Sarin, "Ranking with partial information: A method and an application," Opns. Res. 33 (1985), 38-48. https://doi.org/10.1287/opre.33.1.38
  20. Kmietowicz, Z. W. and A. D. Pearman, "Decision theory, linear partial information and statistical dominance," Omega 12 (1984), 391-399. https://doi.org/10.1016/0305-0483(84)90075-6
  21. Krantz, D. H., R. D. Luce, P. Suppes, and A. Tversky, Foundations of Measurement, Academic Press: New York, 1971.
  22. Lee, K. S., K. S. Park, Y. S. Eum, and K. Park, "Extended methods for identifying dominance and potential optimality in multi-criteria analysis with imprecise information," Eur. J. Opl. Res. 134 (2001), 557-563. https://doi.org/10.1016/S0377-2217(00)00277-0
  23. Malakooti, B., "Ranking and screening multiple criteria alternatives with partial information and use of ordinal and cardinal strength of preferences," IEEE Trans. Syst., Man, Cybern. 30 (2000), 355-368. https://doi.org/10.1109/3468.844359
  24. Mateos, A., S. Rios-Insua, and A. Jimenez, "Dominance, potential optimality and alternative ranking in imprecise multi‐attribute decision making," J. Opl. Res. Soc. 58 (2007), 326-336. https://doi.org/10.1057/palgrave.jors.2602158
  25. Moskowitz, H., P. V. Preckel, and A. Yang, "Multiple‐criteria robust interactive decision analysis (MCRID) for optimizing public policies," Eur. J. Opl. Res. 56 (1992), 219-236. https://doi.org/10.1016/0377-2217(92)90224-W
  26. Park, K. S., "Mathematical programming models for characterizing dominance and potential optimality when multicriteria alternative values and weights are simultaneously incomplete," IEEE Trans. Syst., Man, Cybern., Part A 34 (2004), 601-614. https://doi.org/10.1109/TSMCA.2004.832828
  27. Park, K. S. and S. H. Kim, "Tools for interactive multiattribute decisionmaking with incompletely identified information," Eur. J. Opl. Res. 98 (1997), 111-123. https://doi.org/10.1016/0377-2217(95)00121-2
  28. Pearman, A. D., "Establishing dominance in multiattribute decision making using an ordered metric method," J. Opl. Res. Soc. 44 (1993), 461-469. https://doi.org/10.1057/jors.1993.82
  29. Sage, A. P. and C. C. White III, "ARIADNE: A knowledge-based interactive system for planning and decision support," IEEE Trans. Syst., Man, Cybern. 14 (1984), 35-47.
  30. Salo, A. A. and R. P. Hamalainen, Preference assessment by imprecise ratio statements, Opns. Res. 40 (1992), 1053-1061. https://doi.org/10.1287/opre.40.6.1053
  31. Stewart, T. J., "Relationships between data envelopment analysis and multicriteria decision analysis," J. Opl. Res. Soc. 47 (1996), 654-665. https://doi.org/10.1057/jors.1996.77
  32. von Winterfeldt, D. and W. Edwards, Decision Analysis and Behavioral Research, Cambridge University Press: New York, 1986.
  33. Weber, M., "Decision making with incomplete information," Eur. J. Opl. Res. 28 (1987), 44-57. https://doi.org/10.1016/0377-2217(87)90168-8