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AIMS Mathematics

2022, Volume 7, Issue 8: 14117-14138. doi: 10.3934/math.2022778
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Research article

Novel operations of weighted hesitant fuzzy sets and their group decision making application

  • 1.
    School of Artificial Intelligence, Beijing Normal University, Beijing 100875, China
  • 2.
    Academy of Foundational Education, Neusoft Institute Guangdong, Foshan 528225, China
  • 3.
    Business School, Sichuan University, Chengdu 610065, China
  • 4.
    Mathematics Department, Faculty of Science, Al-Azhar University, Assiut, Egypt
  • Received: 31 March 2022 Revised: 09 May 2022 Accepted: 16 May 2022 Published: 27 May 2022

  • MSC : 68U35

  • Weighted hesitant fuzzy set (WHFS) is an extension of hesitant fuzzy set (HFS), in which the weights indicate that the decision maker has different confidence in giving every possible assessment of the membership degree. In this paper, we redefine the union and intersection operations of weighted hesitant fuzzy elements (WHFEs), investigate their operation properties, and propose the variance function of the weighted hesitant fuzzy element (WHFE) to compare WHFEs. Furthermore, we develop two aggregation operators such as weighted hesitant fuzzy ordered weighted averaging (WHFOWA) and weighted hesitant fuzzy ordered weighted geometric (WHFOWG) operators to aggregate weighted hesitant fuzzy information, and present multiple-attribute group decision making algorithm under weighted hesitant fuzzy environment. Finally, four numerical examples are used to illustrate the effectiveness of our proposed aggregation operators.

    Citation: Wenyi Zeng, Rong Ma, Deqing Li, Qian Yin, Zeshui Xu, Ahmed Mostafa Khalil. Novel operations of weighted hesitant fuzzy sets and their group decision making application[J]. AIMS Mathematics, 2022, 7(8): 14117-14138. doi: 10.3934/math.2022778

    Related Papers:

  • Weighted hesitant fuzzy set (WHFS) is an extension of hesitant fuzzy set (HFS), in which the weights indicate that the decision maker has different confidence in giving every possible assessment of the membership degree. In this paper, we redefine the union and intersection operations of weighted hesitant fuzzy elements (WHFEs), investigate their operation properties, and propose the variance function of the weighted hesitant fuzzy element (WHFE) to compare WHFEs. Furthermore, we develop two aggregation operators such as weighted hesitant fuzzy ordered weighted averaging (WHFOWA) and weighted hesitant fuzzy ordered weighted geometric (WHFOWG) operators to aggregate weighted hesitant fuzzy information, and present multiple-attribute group decision making algorithm under weighted hesitant fuzzy environment. Finally, four numerical examples are used to illustrate the effectiveness of our proposed aggregation operators.


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