Consensus reaching models of linguistic preference relations based on distance functions |
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Authors: | Zhibin Wu Jiuping Xu |
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Affiliation: | (1) Uncertain Decision-making Laboratory, Sichuan University, Chengdu, 610064, China; |
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Abstract: | In group decision making (GDM) using linguistic preference relations to obtain the maximum degree of agreement, it is desirable
to develop a consensus process prior to the selection process. This paper proposes two consensus models with linguistic information
to support the GDM consensus reaching process. Two different distance functions between linguistic preference relations are
introduced to measure both individual consistency and group consensus. Based on these measures, the consensus reaching models
are developed. The two models presented have the same concept that the expert whose preference is farthest from the group
preference needs to update their opinion according to the group preference relation. In addition, the convergence of the models
is proved. After achieving the predefined consensus level, each expert’s consistency indexes are still acceptable under the
condition that the initial preference relations are of satisfactory consistency. Finally, an example is given to show the
effectiveness of the models and to verify the theoretical results. |
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