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Extended hesitant fuzzy hybrid weighted aggregation operators and their application in decision making

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Abstract

Hesitant fuzzy set turns out to be a powerful tool in expressing uncertainty and vagueness. Liao and Xu (J Intell Fuzzy Syst, 26:1601–1617, 2014b) proposed a family of hesitant fuzzy hybrid weighted aggregation operators to synthesize hesitant fuzzy information and pointed out that these operators not only weight the importance of the hesitant fuzzy arguments and their ordered positions simultaneously, but also keep the property of idempotency. In this paper, some new properties, such as the boundedness and commutativity, of these operators are further investigated. After that, several new aggregation operators are introduced, including the generalized hesitant fuzzy hybrid weighted averaging operator, the generalized hesitant fuzzy hybrid weighted geometric operator, the generalized quasi hesitant fuzzy hybrid weighted averaging operator, the generalized quasi hesitant fuzzy hybrid weighted geometric operator, and their induced forms. The properties of these operators are investigated as well. Based on the proposed operators, an algorithm is established to aid multi-criteria decision making with hesitant fuzzy information. A numerical example concerning the evaluation of candidate portfolios is provided to show the practicality and validity of the proposed procedure and aggregation operators.

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Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their insightful and constructive comments and suggestions that have led to this improved version of the paper. The work was supported in part by the National Natural Science Foundation of China (No. 61273209), the Excellent Ph.D. Thesis Foundation of Shanghai Jiao Tong University (No. 20131216), and the Scholarship from China Scholarship Council (No. 201306230047).

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Authors and Affiliations

  1. Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai, 200052, China

    Huchang Liao

  2. Business School, Sichuan University, Chengdu, 610065, Sichuan, China

    Zeshui Xu

Authors
  1. Huchang Liao
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  2. Zeshui Xu
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Correspondence to Zeshui Xu.

Additional information

Communicated by V. Loia.

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Liao, H., Xu, Z. Extended hesitant fuzzy hybrid weighted aggregation operators and their application in decision making. Soft Comput 19, 2551–2564 (2015). https://doi.org/10.1007/s00500-014-1422-6

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  • DOI: https://doi.org/10.1007/s00500-014-1422-6

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