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Additive consistency exploration of linguistic preference relations with self-confidence

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Abstract

Preference relation is one of the most effective tools for decision makers (experts) to express their evaluation information in decision making. Recently, a new type of preference relation called linguistic preference relations with self-confidence (LPRs-SC) has been proposed. In an LPR-SC, experts can express multiple self-confidence levels when providing their preferences. Consistency of preference relations is an important premise for reliable and reasonable decision making. This research mainly focuses on the additive consistency exploration of LPRs-SC. To do that, some operational laws for LPRs-SC are introduced. Subsequently, an additive consistency index which considers both the linguistic preference values and the self-confidence is defined to measure the consistency level of LPR-SC. For an inconsistent LPR-SC, an optimization model and an iterative algorithm are developed to repair its consistency. It is worth noting that the inconsistency repairing methods proposed in this paper consider the acceptable adjustment range of experts, thereby increase their willingness to adjust the preference values and let the experts participate in the consistency improving process. Besides, the presented iterative algorithm is further extended to group decision making with LPRs-SC. Finally, two examples are furnished to demonstrate the feasibility and effectiveness of the proposed methods.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (NSFC) under Grants (71871085, 42171081), and the financial support from the FEDER funds provided in the National Spanish project PID2019-103880RB-I00, and also it has been partially supported by grants from the National Natural Science Foundation of China (NSFC) under Grants (71910107002).

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Authors and Affiliations

  1. Business School, Hohai University, Nanjing, 211100, People’s Republic of China

    Yejun Xu, Shennan Zhu & Jing Huang

  2. Research Center for Green Development of Agriculture, South China Agriculture University, Guang Zhou, 510642, People’s Republic of China

    Yejun Xu

  3. College of Management and Economics, Tianjin University, Tianjin, 300072, People’s Republic of China

    Yejun Xu

  4. School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, People’s Republic of China

    Xia Liu

  5. Dept. of Computer Science and AI, Andalusian Research Institute in Data Science and Computational Intelligence, University of Granada, 18071, Granada, Spain

    Enrique Herrera-Viedma

  6. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Enrique Herrera-Viedma

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  1. Yejun Xu
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  2. Shennan Zhu
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  3. Xia Liu
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  5. Enrique Herrera-Viedma
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Correspondence to Yejun Xu.

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Xu, Y., Zhu, S., Liu, X. et al. Additive consistency exploration of linguistic preference relations with self-confidence. Artif Intell Rev 56, 257–285 (2023). https://doi.org/10.1007/s10462-022-10172-x

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