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Some intuitionistic uncertain linguistic Bonferroni mean operators and their application to group decision making

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Abstract

With respect to multi-attribute group decision-making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables (IULVs), the group decision-making methods based on some Bonferroni mean (BM) aggregation operators were developed. Firstly, we proposed some new operational rules for the IULVs which can overcome the weaknesses of the existing operations. Then, we extended BM operator to the IULVs and developed intuitionistic uncertain linguistic arithmetic Bonferroni mean (IULABM) operator, intuitionistic uncertain linguistic arithmetic weighted Bonferroni mean (IULWABM) operator, intuitionistic uncertain linguistic geometric Bonferroni mean (IULGBM) operator, and intuitionistic uncertain linguistic weighted geometric Bonferroni mean (IULWGBM) operator. At the same time, some desirable properties of the proposed operators, such as idempotency, boundedness, and monotonicity, were studied, and some special cases of these operators were analyzed. Moreover, some approaches based on the developed operators are proposed. Finally, an illustrative example is given to show the steps of the developed methods and to discuss the influences of different parameters on the decision-making results.

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Acknowledgements

This paper is supported by the National Natural Science Foundation of China (Nos. 71771140, 71471172, and 71271124), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045), Shandong Provincial Social Science Planning Project (Nos. 17BGLJ04, 16CGLJ31 and 16CKJJ27), the Natural Science Foundation of Shandong Province (No. ZR2017MG007), the Teaching Reform Research Project of Undergraduate Colleges and Universities in Shandong Province (No. 2015Z057), and Key Research and Development Program of Shandong Province (No. 2016GNC110016). The authors also would like to express appreciation to the anonymous reviewers and editors for their very helpful comments that improved the paper.

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Authors and Affiliations

  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, Shandong, China

    Peide Liu & Xiaohong Zhang

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  1. Peide Liu
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  2. Xiaohong Zhang
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Correspondence to Peide Liu.

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We declare that we do have no commercial or associative interests that represent a conflict of interests in connection with this manuscript. There are no professional or other personal interests that can inappropriately influence our submitted work.

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Communicated by V. Loia.

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Liu, P., Zhang, X. Some intuitionistic uncertain linguistic Bonferroni mean operators and their application to group decision making. Soft Comput 23, 3869–3886 (2019). https://doi.org/10.1007/s00500-018-3048-6

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