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Ranking Objects from Individual Linguistic Dual Hesitant Fuzzy Information in View of Optimal Model-Based Consistency and Consensus Iteration Algorithm

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Abstract

Linguistic variables are flexible and intuitive attraction for expressing the wording of decision makers. This paper introduces a new type of linguistic fuzzy sets called linguistic dual hesitant fuzzy sets to express the hesitancy of decision makers’ qualitative preferences and non-preferences. Considering the application in decision making, linguistic dual hesitant fuzzy preference relations (LDHFPRs) are introduced that permit the decision makers to apply several linguistic variables to indicate a qualitative preferred judgment and a qualitative non-preferred judgment, respectively. To rank objects from LDHFPRs rationally, a consistency concept is first presented. Then, two optimal models are built to judge the consistency of LDHFPRs. When LDHFPRs are inconsistent, an optimal model-based iteration algorithm for obtaining consistent LDHFPRs is offered. Based on consistent linguistic intuitionistic fuzzy preference relations, a method for calculating the weighted linguistic intuitionistic fuzzy priority vector is introduced. In the setting of group decision making (GDM), a consensus measure based on individually weighted consistent reverse complementary linguistic intuitionistic fuzzy preference relations is defined. When the consensus does not satisfy the requirement, a two-step optimal model-based method for increasing the consensus level is offered. Furthermore, an approach for GDM with LDHFPRs is developed. Finally, an illustrative example concerning the evaluation of basic services internet enterprise websites is provided to show the efficiency of the new method.

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Acknowledgements

The work was supported by the Natural Science Foundation of Changsha in China (No. kq2202112), and the Startup Foundation for Introducing Talent of NUIST (No. 2022r059), National Social Science Fund Project (No. 19BGL064), and the Startup Foundation for Introducing Talent of NUIST (No. 2020r001).

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Authors and Affiliations

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

    Fanyong Meng & Jie Tang

  2. School of Accounting, Hunan University of Technology and Business, No. 569, Yuelu Avenue, Changsha, 410205, China

    Aiqing Zeng

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada

    Witold Pedrycz

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  1. Fanyong Meng
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  2. Aiqing Zeng
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Correspondence to Aiqing Zeng.

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Meng, F., Zeng, A., Tang, J. et al. Ranking Objects from Individual Linguistic Dual Hesitant Fuzzy Information in View of Optimal Model-Based Consistency and Consensus Iteration Algorithm. Group Decis Negot 32, 5–44 (2023). https://doi.org/10.1007/s10726-022-09797-8

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