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On Extending Power-Geometric Operators to Interval-Valued Hesitant Fuzzy Sets and Their Applications to Group Decision Making

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Listed:
  • Sheng-Hua Xiong

    (School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, Sichuan 610031, People’s Republic of China)

  • Zhen-Song Chen

    (School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, Sichuan 610031, People’s Republic of China)

  • Yan-Lai Li

    (School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, Sichuan 610031, People’s Republic of China)

  • Kwai-Sang Chin

    (Department of System Engineering and Engineering Management, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, People’s Republic of China)

Abstract

Developing aggregation operators for interval-valued hesitant fuzzy sets (IVHFSs) is a technological task we are faced with, because they are specifically important in many problems related to the fusion of interval-valued hesitant fuzzy information. This paper develops several novel kinds of power geometric operators, which are referred to as variable power geometric operators, and extends them to interval-valued hesitant fuzzy environments. A series of generalized interval-valued hesitant fuzzy power geometric (GIVHFG) operators are also proposed to aggregate the IVHFSs to model mandatory requirements. One of the important characteristics of these operators is that objective weights of input arguments are variable with the change of a non-negative parameter. By adjusting the exact value of the parameter, the influence caused by some “false” or “biased” arguments can be reduced. We demonstrate some desirable and useful properties of the proposed aggregation operators and utilize them to develop techniques for multiple criteria group decision making with IVHFSs considering the heterogeneous opinions among individual decision makers. Furthermore, we propose an entropy weights-based fitting approach for objectively obtaining the appropriate value of the parameter. Numerical examples are provided to illustrate the effectiveness of the proposed techniques.

Suggested Citation

  • Sheng-Hua Xiong & Zhen-Song Chen & Yan-Lai Li & Kwai-Sang Chin, 2016. "On Extending Power-Geometric Operators to Interval-Valued Hesitant Fuzzy Sets and Their Applications to Group Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1055-1114, September.
    • Handle: RePEc:wsi:ijitdm:v:15:y:2016:i:05:n:s0219622016500255
    DOI: 10.1142/S0219622016500255
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    References listed on IDEAS

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    1. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
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