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Discussing incomplete 2-tuple fuzzy linguistic preference relations in multi-granular linguistic MCGDM with unknown weight information

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Abstract

Owing to the vagueness of real-world environments and limited knowledge of human beings, it is natural for decision makers to express their preferences by means of incomplete 2-tuple fuzzy linguistic preference relations (FLPRs). Besides, since different decision makers possess distinctive educational and academic background, they may select linguistic term sets with different granularities to represent their opinions. This study primarily focuses on multi-granular linguistic multi-criteria group decision-making (MCGDM) based on incomplete 2-tuple FLPRs. First, we introduce an extended four-way procedure for estimating unknown elements from an acceptable incomplete 2-tuple FLPR as well as a completion method for obtaining unknown linguistic 2-tuples in an unacceptable incomplete 2-tuple FLPR. Based on the four ways for estimating unknown values, a formula is then established to calculate the consistency index of an incomplete 2-tuple FLPR. Second, a 2-tuple linguistic induced generalized ordered weighted averaging operator is introduced and further analyzed from different aspects. Subsequently, by systematically fusing the aforementioned contributions, a novel approach is developed to address MCGDM problems with multi-granular incomplete 2-tuple FLPRs and unknown weight information. Specifically, the importance weights of decision makers with respect to different criteria are decided by the corresponding consistency indices. Finally, an investment problem is furnished to illustrate the application of our proposed approach.

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Acknowledgements

The authors are rather grateful to thank the editors and anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China (No. 71571193) and the Fundamental Research Funds for the Central Universities of Central South University (2017zzts047).

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  1. School of Business, Central South University, Changsha, 410083, People’s Republic of China

    Xue-yang Zhang, Hong-yu Zhang & Jian-qiang Wang

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  1. Xue-yang Zhang
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  2. Hong-yu Zhang
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Correspondence to Jian-qiang Wang.

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Communicated by V. Loia.

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Zhang, Xy., Zhang, Hy. & Wang, Jq. Discussing incomplete 2-tuple fuzzy linguistic preference relations in multi-granular linguistic MCGDM with unknown weight information. Soft Comput 23, 2015–2032 (2019). https://doi.org/10.1007/s00500-017-2915-x

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