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Novel consistency and consensus of generalized intuitionistic fuzzy preference relations with application in group decision making

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Abstract

Preference relations are an efficient technology to derive the priority vectors for the alternatives in group decision-making. In this paper, an analysis of the existing research on group decision-making with intuitionistic fuzzy preference relations (IFPRs) indicates that IFPRs have some desirable properties similar to those in fuzzy situation. Then, generalized intuitionistic fuzzy preference relations (GIFPRs) and their consistency are proposed to model all those desirable properties. The given consistent GIFPRs are completely characterized by intuitionistic fuzzy priority vectors (IFPVs). For inconsistent GIFPRs, the novel \( \delta \)-acceptable consistency and consensus are proposed to preserve the original preference information as much as possible and methods without thresholds seeking to reach the desirable requirements are provided and visualized. Some numerical examples are given to illustrate the proposed models work; and comparisons with the existing methods are also offered to demonstrate the validity, applicability and advantages of the proposed method.

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Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their insightful and constructive comments and suggestions that have led to this improved version of the paper. This research was supported by the National Research Foundation of Korea funded by the Ministry of Education under Grant NRF-2021R1A2C1095739 and the Natural Science Foundation of Shandong Province (Grant No. ZR2017MG027).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Linyi University, 276005, Linyi, China

    Huan Tian Xie, Zhen Ming Ma & Wei Yang

  2. Business School, Sichuan University, 610064, Chengdu, China

    Ze Shui Xu

  3. Department of Computer Science, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseongsi, Gyeonggi-do, 445-743, Korea

    Zun Wei Fu

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  1. Huan Tian Xie
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  2. Zhen Ming Ma
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  5. Wei Yang
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Correspondence to Zhen Ming Ma.

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Xie, H.T., Ma, Z.M., Xu, Z.S. et al. Novel consistency and consensus of generalized intuitionistic fuzzy preference relations with application in group decision making. Appl Intell 52, 16832–16851 (2022). https://doi.org/10.1007/s10489-021-03081-z

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