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An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application

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  • Sun, Bingzhen
  • Ma, Weimin

Abstract

This paper studies the group decision making problem with linguistic preference relations. We first study the consensus measure between the individual preference relations and the collective (group) preference relation by defining the concept of degree of similarity between two linguistic values and two linguistic preference relations. Then we propose a concept of the acceptance consensus threshold value for group decision making with linguistic preference information. We show that the consensus between individual preference relations and the collective (group) preference relation is greater than the weighted similarity degree of a given individual preference relation with respect to other individual preference relations in group decision making with linguistic preference relations. The results will help in the analysis of crucial issues of conflict and agreement among preferences of decision-makers, which affect the consensus of group decision making with linguistic preference relations. Theoretical foundations are then established for the proposed method. Finally, the proposed method is applied to evaluate the degree of consensus of individual overall preference values with respect to the collective overall preference values for multi-attribute group decision making with linguistic information. The main contribution of this paper is twofold. One is to present a new way to measure the consensus between the individual preference relations and the collective (group) preference relation in group decision making with linguistic preference information. Another is to provide an effective approach to evaluating individual overall preference values with respect to the collective overall preference values in multi-attribute group decision making with linguistic information.

Suggested Citation

  • Sun, Bingzhen & Ma, Weimin, 2015. "An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application," Omega, Elsevier, vol. 51(C), pages 83-92.
    • Handle: RePEc:eee:jomega:v:51:y:2015:i:c:p:83-92
    DOI: 10.1016/j.omega.2014.09.006
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    1. Chang, Sheng-Lin & Wang, Reay-Chen & Wang, Shih-Yuan, 2007. "Applying a direct multi-granularity linguistic and strategy-oriented aggregation approach on the assessment of supply performance," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1013-1025, March.
    2. Hatami-Marbini, Adel & Tavana, Madjid, 2011. "An extension of the Electre I method for group decision-making under a fuzzy environment," Omega, Elsevier, vol. 39(4), pages 373-386, August.
    3. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi, 2008. "On consistency measures of linguistic preference relations," European Journal of Operational Research, Elsevier, vol. 189(2), pages 430-444, September.
    4. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    5. Ma, Li-Ching, 2012. "Screening alternatives graphically by an extended case-based distance approach," Omega, Elsevier, vol. 40(1), pages 96-103, January.
    6. Franco, L. Alberto & Lord, Ewan, 2011. "Understanding multi-methodology: Evaluating the perceived impact of mixing methods for group budgetary decisions," Omega, Elsevier, vol. 39(3), pages 362-372, June.
    7. Morais, Danielle C. & de Almeida, Adiel Teixeira, 2012. "Group decision making on water resources based on analysis of individual rankings," Omega, Elsevier, vol. 40(1), pages 42-52, January.
    8. Zeshui Xu, 2006. "A Practical Procedure for Group Decision Making under Incomplete Multiplicative Linguistic Preference Relations," Group Decision and Negotiation, Springer, vol. 15(6), pages 581-591, November.
    9. Xu, Zeshui, 2005. "Deviation measures of linguistic preference relations in group decision making," Omega, Elsevier, vol. 33(3), pages 249-254, June.
    10. Fu, Chao & Yang, Shanlin, 2012. "An evidential reasoning based consensus model for multiple attribute group decision analysis problems with interval-valued group consensus requirements," European Journal of Operational Research, Elsevier, vol. 223(1), pages 167-176.
    11. Wan, Shu-Ping & Li, Deng-Feng, 2013. "Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees," Omega, Elsevier, vol. 41(6), pages 925-940.
    12. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Feng, Bo, 2010. "The OWA-based consensus operator under linguistic representation models using position indexes," European Journal of Operational Research, Elsevier, vol. 203(2), pages 455-463, June.
    13. Ramanathan, R. & Ganesh, L. S., 1994. "Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members' weightages," European Journal of Operational Research, Elsevier, vol. 79(2), pages 249-265, December.
    14. Pang, Jifang & Liang, Jiye, 2012. "Evaluation of the results of multi-attribute group decision-making with linguistic information," Omega, Elsevier, vol. 40(3), pages 294-301.
    15. Wade D. Cook & Lawrence M. Seiford, 1982. "On the Borda-Kendall Consensus Method for Priority Ranking Problems," Management Science, INFORMS, vol. 28(6), pages 621-637, June.
    16. Kacprzyk, Janusz & Fedrizzi, Mario, 1988. "A `soft' measure of consensus in the setting of partial (fuzzy) preferences," European Journal of Operational Research, Elsevier, vol. 34(3), pages 316-325, March.
    17. F. J. Cabrerizo & S. Alonso & E. Herrera-Viedma, 2009. "A Consensus Model For Group Decision Making Problems With Unbalanced Fuzzy Linguistic Information," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 109-131.
    18. Kreye, M.E. & Goh, Y.M. & Newnes, L.B. & Goodwin, P., 2012. "Approaches to displaying information to assist decisions under uncertainty," Omega, Elsevier, vol. 40(6), pages 682-692.
    19. Verdecho, María-José & Alfaro-Saiz, Juan-Jose & Rodriguez-Rodriguez, Raul & Ortiz-Bas, Angel, 2012. "A multi-criteria approach for managing inter-enterprise collaborative relationships," Omega, Elsevier, vol. 40(3), pages 249-263.
    20. Huang, Yeu-Shiang & Chang, Wei-Chen & Li, Wei-Hao & Lin, Zu-Liang, 2013. "Aggregation of utility-based individual preferences for group decision-making," European Journal of Operational Research, Elsevier, vol. 229(2), pages 462-469.
    21. Kadziński, Miłosz & Greco, Salvatore & Słowiński, Roman, 2013. "RUTA: A framework for assessing and selecting additive value functions on the basis of rank related requirements," Omega, Elsevier, vol. 41(4), pages 735-751.
    22. Doukas, Haris, 2013. "Modelling of linguistic variables in multicriteria energy policy support," European Journal of Operational Research, Elsevier, vol. 227(2), pages 227-238.
    23. Wang, Shih-Yuan & Chang, Sheng-Lin & Wang, Reay-Chen, 2009. "Assessment of supplier performance based on product-development strategy by applying multi-granularity linguistic term sets," Omega, Elsevier, vol. 37(1), pages 215-226, February.
    24. Kim, Soung Hie & Choi, Sang Hyun & Kim, Jae Kyeong, 1999. "An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach," European Journal of Operational Research, Elsevier, vol. 118(1), pages 139-152, October.
    25. Fu, Chao & Yang, Shanlin, 2011. "An attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context," European Journal of Operational Research, Elsevier, vol. 212(1), pages 179-189, July.
    26. Z Xu & M Xia, 2014. "Iterative algorithms for improving consistency of intuitionistic preference relations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(5), pages 708-722, May.
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