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Analysis of acceptable additive consistency and consensus of group decision making with interval-valued hesitant fuzzy preference relations

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Abstract

Interval-valued hesitant fuzzy sets are efficient to denote the hesitant and uncertain judgments of decision makers. To further research the utilization of this type of fuzzy sets, this paper limits to study group decision making (GDM) with interval-valued hesitant fuzzy preference relations (IVHFPRs). First, an additive consistency index is defined for interval fuzzy preference relations, by which we derive a new acceptable additive consistency concept for IVHFPRs. Then, new models based on acceptable additive consistency are built for ascertaining unknown values, and new models for judging the acceptable additive consistency of IVHFPRs are constructed. When the consistency of IVHFPRs is unacceptable, new models based on consistency and uncertain degree are constructed for obtaining acceptable additive consistency IVHFPRs that can ensure the smallest total adjustment and the minimum number of adjusted intervals. For GDM case, a new consensus index is defined to measure the agreement degree of individual judgments. When the consensus level does not satisfy requirement, new models for reaching the additive consistency and consensus requirements are built. Furthermore, a new acceptable additive consistency- and consensus-based algorithm for GDM with incomplete and unacceptable additive consistency IVHFPRs is provided. Finally, an example is given to indicate the utilization of the new algorithm and comparison analysis is made.

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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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Author notes

  1. Fanyong Meng

    Present address: School of Management Science and Engineering, Nanjing University of Information Science and Technology, No.219, Ningliu Road, Jiangsu, 210044, People’s Republic of China

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. Faculty of Information Technology, Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam

    Hamido Fujita

  3. Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI), University of Granada, Granada, Spain

    Hamido Fujita

  4. Faculty of Software and Information Science, Iwate Prefectural University, Iwate, 020-0693, Japan

    Hamido Fujita

  5. Guanghua Management School, Peking University, Beijing, 100871, China

    Xiaodan Zhang

  6. School of Management and Economics, Beijing Institute of Technology, Beijing, 100081, China

    Yunning Zhang

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  1. Jie Tang
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  3. Hamido Fujita
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  4. Xiaodan Zhang
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Correspondence to Fanyong Meng.

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Tang, J., Zhang, Y., Fujita, H. et al. Analysis of acceptable additive consistency and consensus of group decision making with interval-valued hesitant fuzzy preference relations. Neural Comput & Applic 33, 7747–7772 (2021). https://doi.org/10.1007/s00521-020-05516-z

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