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A group decision making approach for trapezoidal fuzzy preference relations with compatibility measure

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Abstract

The purpose of this paper is to develop a new compatibility for the additive trapezoidal fuzzy preference relations and utilize it to determine the optimal weights of experts in the group decision making. First, a least deviation model to obtain the priority vector of the additive trapezoidal fuzzy preference relation is provided. Then compatibility index of two additive trapezoidal fuzzy preference relations is proposed and some desirable properties are investigated. The characteristic of the new compatibility is that it uses the deviation measure between an additive trapezoidal fuzzy preference relation and its characteristic preference relation based on consistency of the preference relation, which develops a theoretic basis for the application of additive trapezoidal fuzzy preference relations in group decision making. Then, in order to determine the weights of experts in the group decision making, we propose an optimal model based on the criterion of minimizing the compatibility index. Finally, an example shows the feasibility and effectiveness of the proposed method.

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Acknowledgments

The authors would like to thank the editor and anonymous referees for their insightful and constructive comments and suggestions that have led to an improved version of this paper. The work was supported by National Natural Science Foundation of China (Nos. 71301001, 71371011, 71501002), Higher School Specialized Research Fund for the Doctoral Program (No. 20123401110001), Project of Anhui Province for Excellent Young Talents. The Doctoral Scientific Research Foundation of Anhui University. Anhui Provincial Natural Science Foundation (No. 1308085QG127), Humanity and Social Science Youth Foundation of Ministry of Education (No. 13YJC630092), The Scientific Research and Development Foundation of Hefei University (No. 12KY02ZD) and Provincial Natural Science Research Project of Anhui Colleges (No. KJ2015A379).

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Authors and Affiliations

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

    Yuanyuan Zhou, Ligang Zhou & Huayou Chen

  2. Department of Mathematics and Physics, Hefei University, Hefei, 230601, Anhui, China

    Linghua Cheng

  3. Department of Electrical Engineering, Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, 90089, USA

    Ligang Zhou

  4. Hefei No. 1 High School, Hefei, 230001, Anhui, China

    Jianqiao Ge

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  1. Yuanyuan Zhou
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  2. Linghua Cheng
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Correspondence to Ligang Zhou.

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Communicated by V. Loia.

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Zhou, Y., Cheng, L., Zhou, L. et al. A group decision making approach for trapezoidal fuzzy preference relations with compatibility measure. Soft Comput 21, 2709–2721 (2017). https://doi.org/10.1007/s00500-015-1975-z

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