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Linguistic Interval Hesitant Fuzzy Sets and Their Application in Decision Making

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Abstract

To cope with the hesitancy and uncertainty of the decision makers’ cognitions to decision-making problems, this paper introduces a new type of fuzzy sets called linguistic interval hesitant fuzzy sets. A linguistic interval hesitant fuzzy set is composed of several linguistic terms with each one having several interval membership degrees. Considering the application of linguistic interval hesitant fuzzy sets in decision making, an ordered relationship is offered, and several operational laws are defined. After that, several aggregation operators based on additive and fuzzy measures are introduced, by which the comprehensive attribute values can be obtained. Based on the defined distance measure, models for the optimal weight vectors are constructed. In addition, an approach to multi-attribute decision making with linguistic interval hesitant fuzzy information is developed. Finally, two numerical examples are provided to show the concrete application of the procedure.

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Acknowledgments

The authors first want to thank the Editor-in-Chief Professor Amir Hussain, the associate Editor and five anonymous referees for their constructive and valuable comments, which have much improved the paper. This work was supported by the State Key Program of National Natural Science of China (No. 71431006), the Funds for Creative Research Groups of China (No. 71221061), the Projects of Major International Cooperation NSFC (No. 71210003), the National Natural Science Foundation of China (Nos. 71201089, 71201110, 71271217 and 71271029), the National Science Foundation for Post-doctoral Scientists of China (2014M560655) and the Program for New Century Excellent Talents in University of China (No. NCET-12-0541).

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  1. Business School, Central South University, Changsha, 410083, China

    Fanyong Meng & Xiaohong Chen

  2. School of Management, Qingdao Technological University, Qingdao, 266520, China

    Fanyong Meng & Chen Wang

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  1. Fanyong Meng
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Meng, F., Wang, C. & Chen, X. Linguistic Interval Hesitant Fuzzy Sets and Their Application in Decision Making. Cogn Comput 8, 52–68 (2016). https://doi.org/10.1007/s12559-015-9340-1

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