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Compatible weighting method with rank order centroid: Maximum entropy ordered weighted averaging approach

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  • Ahn, Byeong Seok

Abstract

In a situation where imprecise attribute weights such as a rank order are captured, various approximate weighting methods have been proposed to aid multiattribute decision analysis. Among others, it is well known that the rank order centroid (ROC) weights result in the highest performance in terms of the identification of the best alternative under the ranked attribute weights. In this paper, we aim to reinterpret the meaning of the ROC weights and to develop a compatible weighting method that is based on other well-established academic disciplines. The ordered weighted averaging (OWA) method is a nonlinear aggregation method in that the weights are associated with the objects reordered according to their magnitudes in the aggregation process. Some interesting semantics can be attached to the approximate weights in view of the measure developed in the OWA method. Furthermore, the weights generated by the maximum entropy method show equally compatible performance with the ROC weights under some condition, which is demonstrated by theoretical and simulation analysis.

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  • Ahn, Byeong Seok, 2011. "Compatible weighting method with rank order centroid: Maximum entropy ordered weighted averaging approach," European Journal of Operational Research, Elsevier, vol. 212(3), pages 552-559, August.
    • Handle: RePEc:eee:ejores:v:212:y:2011:i:3:p:552-559
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    1. Craig W. Kirkwood & Rakesh K. Sarin, 1985. "Ranking with Partial Information: A Method and an Application," Operations Research, INFORMS, vol. 33(1), pages 38-48, February.
    2. Zarghami, Mahdi & Szidarovszky, Ferenc, 2009. "Revising the OWA operator for multi criteria decision making problems under uncertainty," European Journal of Operational Research, Elsevier, vol. 198(1), pages 259-265, October.
    3. Weber, Martin, 1987. "Decision making with incomplete information," European Journal of Operational Research, Elsevier, vol. 28(1), pages 44-57, January.
    4. Jaccard, James & Brinberg, David & Ackerman, Lee J, 1986. "Assessing Attribute Importance: A Comparison of Six Methods," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 12(4), pages 463-468, March.
    5. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    6. Wade D. Cook & Moshe Kress, 1990. "A Data Envelopment Model for Aggregating Preference Rankings," Management Science, INFORMS, vol. 36(11), pages 1302-1310, November.
    7. Olson, D. L. & Dorai, V. K., 1992. "Implementation of the centroid method of Solymosi and Dombi," European Journal of Operational Research, Elsevier, vol. 60(1), pages 117-129, July.
    8. F. Hutton Barron & Bruce E. Barrett, 1996. "Decision Quality Using Ranked Attribute Weights," Management Science, INFORMS, vol. 42(11), pages 1515-1523, November.
    9. Fischer, Gregory W., 1995. "Range Sensitivity of Attribute Weights in Multiattribute Value Models," Organizational Behavior and Human Decision Processes, Elsevier, vol. 62(3), pages 252-266, June.
    10. Edwards, Ward & Barron, F. Hutton, 1994. "SMARTS and SMARTER: Improved Simple Methods for Multiattribute Utility Measurement," Organizational Behavior and Human Decision Processes, Elsevier, vol. 60(3), pages 306-325, December.
    11. Keeney,Ralph L. & Raiffa,Howard, 1993. "Decisions with Multiple Objectives," Cambridge Books, Cambridge University Press, number 9780521438834, January.
    12. Figueira, Jose & Roy, Bernard, 2002. "Determining the weights of criteria in the ELECTRE type methods with a revised Simos' procedure," European Journal of Operational Research, Elsevier, vol. 139(2), pages 317-326, June.
    13. Peter C. Fishburn, 1965. "Analysis of Decisions with Incomplete Knowledge of Probabilities," Operations Research, INFORMS, vol. 13(2), pages 217-237, April.
    14. Ribeiro, Rita Almeida & Marques Pereira, Ricardo Alberto, 2003. "Generalized mixture operators using weighting functions: A comparative study with WA and OWA," European Journal of Operational Research, Elsevier, vol. 145(2), pages 329-342, March.
    15. Kirkwood, Craig W. & Corner, James L., 1993. "The Effectiveness of Partial Information about Attribute Weights for Ranking Alternatives in Multiattribute Decision Making," Organizational Behavior and Human Decision Processes, Elsevier, vol. 54(3), pages 456-476, April.
    16. Paul J. H. Schoemaker & C. Carter Waid, 1982. "An Experimental Comparison of Different Approaches to Determining Weights in Additive Utility Models," Management Science, INFORMS, vol. 28(2), pages 182-196, February.
    17. Canós, L. & Liern, V., 2008. "Soft computing-based aggregation methods for human resource management," European Journal of Operational Research, Elsevier, vol. 189(3), pages 669-681, September.
    18. Park, Kyung Sam & Kim, Soung Hie, 1997. "Tools for interactive multiattribute decisionmaking with incompletely identified information," European Journal of Operational Research, Elsevier, vol. 98(1), pages 111-123, April.
    19. Kmietowicz, ZW & Pearman, AD, 1984. "Decision theory, linear partial information and statistical dominance," Omega, Elsevier, vol. 12(4), pages 391-399.
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