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On compatibility of uncertain multiplicative linguistic preference relations based on the linguistic COWGA

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Abstract

The aim of this work is to develop a new compatibility for the uncertain multiplicative linguistic preference relations and utilize it to determine the optimal weights of experts in the group decision making (GDM). First, the compatibility degree and compatibility index for the two multiplicative linguistic preference relations are proposed. Then, based on the linguistic continuous ordered weighted geometric averaging (LCOWGA) operator, some concepts of the compatibility degree and compatibility index for the two uncertain multiplicative linguistic preference relations are presented. We prove the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that the uncertain multiplicative linguistic preference relations given by experts are all of acceptable compatibility with the ideal uncertain multiplicative linguistic preference relation, which provides a theoretic basis for the application of the uncertain multiplicative linguistic preference relations in GDM. Next, an optimal model is constructed to determine the weights of experts based on the criterion of minimizing the compatibility index in GDM. Moreover, an approach to GDM with uncertain multiplicative linguistic preference relations is developed, and finally, an application of the approach to supplier selection problem with uncertain multiplicative linguistic preference relations is pointed out.

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Acknowledgements

The work was supported by National Natural Science Foundation of China (No. 71071002), Higher School Specialized Research Fund for the Doctoral Program (No. 20123401110001), The Scientific Research Foundation of the Returned Overseas Chinese Scholars, Anhui Provincial Natural Science Foundation (No. 1308085QG127), Provincial Natural Science Research Project of Anhui Colleges (No. KJ2012A026), Humanity and Social Science Youth foundation of Ministry of Education (No. 13YJC630092), Humanities and social science Research Project of Department of Education of Anhui Province (No. SK2013B041). The authors are very grateful to the anonymous reviewers and the editor for their insightful and constructive comments and suggestions that have led to an improved version of this paper.

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  1. School of Mathematical Science, Anhui University, Hefei, Anhui, 230601, China

    Ligang Zhou, Yingdong He & Huayou Chen

  2. School of Business, Anhui University, Hefei, Anhui, 230601, China

    Jinpei Liu

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  1. Ligang Zhou
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Correspondence to Huayou Chen.

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Zhou, L., He, Y., Chen, H. et al. On compatibility of uncertain multiplicative linguistic preference relations based on the linguistic COWGA. Appl Intell 40, 229–243 (2014). https://doi.org/10.1007/s10489-013-0454-4

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