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Common probability-based interactive algorithms for group decision making with normalized probability linguistic preference relations

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Abstract

Probabilistic linguistic variable is a kind of powerful qualitative fuzzy sets, which permits the decision makers (DMs) to apply several linguistic variables with probabilities to denote a judgment. This paper studies group decision making (GDM) with normalized probability linguistic preference relations (NPLPRs). To achieve this goal, an acceptably multiplicative consistency based interactive algorithm is provided to derive common probability linguistic preference relations (CPLPRs) from PLPRs, by which a new acceptably multiplicative consistency concept for NPLPRs is defined. When the multiplicative consistency of NPLPRs is unacceptable, models for deriving acceptably multiplicatively consistent NPLPRs are constructed. Then, it studies incomplete NPLPRs (InNPLPRs) and offers a common probability and acceptably multiplicative consistency based interactive algorithm to determine missing judgments. Furthermore, a correlation coefficient between CPLPRs is provided, by which the weights of the DMs are ascertained. Meanwhile, a consensus index based on CPLPRs is defined. When the consensus does not reach the requirement, a model to increase the level of consensus is built that can ensure the adjusted LPRs to meet the multiplicative consistency and consensus requirement. Moreover, an interactive algorithm for GDM with NPLPRs is provided, which can address unacceptably multiplicatively consistent InNPLPRs. Finally, an example about the evaluation of green design schemes for new energy vehicles is provided to indicate the application of the new algorithm and comparative analysis is conducted.

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References

  • Alonso, S., Cabrerizo, F. J., Chiclana, F., Herrera, F., & Herrera-Viedma, E. (2009). Group decision making with incomplete fuzzy linguistic preference relations. International Journal of Intelligent Systems, 24, 201–222.

    Article  Google Scholar 

  • Alonso, S., Chiclana, F., Herrera, F., Herrera-Viedma, E., Alcala-Fdez, J., & Porcelet, C. (2008). A consistency-based procedure to estimate missing pairwise preference values. International Journal of Intelligent Systems, 23, 155–175.

    Article  Google Scholar 

  • Dong, Y. C., Hong, W. C., & Xu, Y. (2013). Measuring consistency of linguistic preference relations: A 2-tuple linguistic approach. Soft Computing, 17, 2117–2130.

    Article  Google Scholar 

  • Dong, Y. C., Xu, Y. F., & Li, H. Y. (2008). On consistency measures of linguistic preference relations. European Journal of Operational Research, 189, 430–444.

    Article  MathSciNet  Google Scholar 

  • Gao, J., Xu, Z. S., Liang, Z. L., & Liao, H. C. (2019a). Expected consistency-based emergency decision making with incomplete probabilistic linguistic preference relations. Knowledge-Based Systems, 176, 15–28.

    Article  Google Scholar 

  • Gao, J., Xu, Z. S., Ren, P. J., & Liao, H. C. (2019b). An emergency decision making method based on the multiplicative consistency of probabilistic linguistic preference relations. International Journal of Machine Learning and Cybernetics, 10, 1613–1629.

    Article  Google Scholar 

  • Herrera, F., & Herrera-Viedma, E. (2000). Choice functions and mechanisms for linguistic preference relations. European Journal of Operational Research, 120, 144–161.

    Article  MathSciNet  Google Scholar 

  • Herrera, F., Herrera-Viedma, E., & Verdegay, J. L. (1996). A model of consensus in group decision making under linguistic assessments. Fuzzy Sets and Systems, 78, 73–87.

    Article  MathSciNet  Google Scholar 

  • Herrera-Viedma, E., Martinez, L., Mata, F., & Chiclana, F. (2005). A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Transactions on Fuzzy Systems, 13, 644–658.

    Article  Google Scholar 

  • Liao, H. C., Jiang, L. S., Lev, B., & Fujita, H. (2019). Novel operations of PLTSs based on the disparity degrees of linguistic terms and their use in designing the probabilistic linguistic ELECTRE III method. Applied Soft Computing, 80, 450–464.

    Article  Google Scholar 

  • Liu, P. D., & Li, Y. (2019). An extended MULTIMOORA method for probabilistic linguistic multi-criteria group decision-making based on prospect theory. Computers & Industrial Engineering, 136, 528–545.

    Article  Google Scholar 

  • Meng, F. Y., Tang, J., & Zhang, Y. L. (2019). Programming model-based group decision making with multiplicative linguistic intuitionistic fuzzy preference relations. Computers & Industrial Engineering, 136, 212–224.

    Article  Google Scholar 

  • Pang, Q., Wang, H., & Xu, Z. S. (2016). Probabilistic linguistic term sets in multi-attribute group decision making. Information Sciences, 369, 128–143.

    Article  Google Scholar 

  • Rodriguez, R. M., Martinez, L., & Herrera, F. (2011). Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on Fuzzy Systems, 20, 109–119.

    Article  Google Scholar 

  • Song, Y. M., & Hu, J. (2019). Large-scale group decision making with multiple stakeholders based on probabilistic linguistic preference relation. Applied Soft Computing, 80, 712–722.

    Article  Google Scholar 

  • Tang, X. A., Zhang, Q., Peng, Z. L., Pedrycz, W., & Yang, S. L. (2020). Distribution linguistic preference relations with incomplete symbolic proportions for group decision making. Applied Soft Computing, 88, 106005.

    Article  Google Scholar 

  • Tanino, T. (1984). Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems, 33, 117–131.

    Article  MathSciNet  Google Scholar 

  • Wu, X. L., & Liao, H. C. (2018). An approach to quality function deployment based on probabilistic linguistic term sets and ORESTE method for multi-expert multi-criteria decision making. Information Fusion, 43, 13–26.

    Article  Google Scholar 

  • Xia, M. M., Xu, Z. S., & Wang, Z. (2014). Multiplicative consistency-based decision support system for incomplete linguistic preference relations. International Journal of Systems Science, 45, 625–636.

    Article  MathSciNet  Google Scholar 

  • Xu, Z. S. (2004a). EOWA, EOWG operators for aggregating linguistic labels based on linguistic preference relations. International Journal of Uncertainty Fuzziness and Knowledge-based Systems, 12, 791–810.

    Article  MathSciNet  Google Scholar 

  • Xu, Z. S. (2004b). Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Information Sciences, 168, 171–184.

    Article  Google Scholar 

  • Zadeh, L. A. (1975). The concept of a linguistic variable, its application to approximate reasoning-part I. Information Sciences, 8, 199–249.

    Article  Google Scholar 

  • Zhang, G. Q., Dong, Y. C., & Xu, Y. F. (2014). Consistency and consensus measures for linguistic preference relations based on distribution assessments. Information Fusion, 17, 46–55.

    Article  Google Scholar 

  • Zhang, Y. X., Xu, Z. S., Wang, H., & Liao, H. C. (2016). Consistency-based risk assessment with probabilistic linguistic preference relation. Applied Soft Computing, 49, 817–833.

    Article  Google Scholar 

  • Zhu, B., & Xu, Z. S. (2014). Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Transactions on Fuzzy Systems, 22, 35–45.

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Startup Foundation for Introducing Talent of NUIST (No. 2020r001), the National Natural Science Foundation of China (No. 71571192), and the Beijing Intelligent Logistics System Collaborative Innovation Center (No. 2019KF-09).

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Authors and Affiliations

  1. School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Jie Tang & Fanyong Meng

  2. School of Automobiles, Qingdao Technological University, Qingdao, 262500, China

    Yongliang Zhang

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  1. Jie Tang
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  2. Fanyong Meng
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Correspondence to Yongliang Zhang.

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Tang, J., Meng, F. & Zhang, Y. Common probability-based interactive algorithms for group decision making with normalized probability linguistic preference relations. Fuzzy Optim Decis Making 21, 99–136 (2022). https://doi.org/10.1007/s10700-021-09360-1

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