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Multiple Attribute Decision-Making Based on Three-Parameter Generalized Weighted Heronian Mean

Author

Listed:
  • Ximei Hu

    (School of Economics and Management, North China Electric Power University, Beijing 102206, China)

  • Shuxia Yang

    (School of Economics and Management, North China Electric Power University, Beijing 102206, China)

  • Ya-Ru Zhu

    (Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China)

Abstract

For the aggregation problem of attributes with a correlation relationship, it is often necessary to take the correlation factor into account in order to make the decision results more objective and reasonable. The Heronian mean is an aggregation operator which reflects the interaction between attributes. It is of great theoretical and practical significance to study and popularize the multiple attribute decision-making methods based on the Heronian mean operator. In this paper, we first give a new three-parameter generalized weighted Heronian mean (TPGWHM), which has a series of excellent properties such as idempotency, monotonicity and boundedness. At the same time, the relationship between the TPGWHM and the existing aggregation operators is given. Then, we propose the intuitionistic fuzzy three-parameter generalized weighted Heronian mean (IFTPGWHM) and give its idempotency, monotonicity, boundedness and limit properties. On this basis, a multiple attribute decision-making method based on the TPGWHM and a multiple attribute decision-making method based on the IFTPGWHM are given, and corresponding examples are given and analyzed.

Suggested Citation

  • Ximei Hu & Shuxia Yang & Ya-Ru Zhu, 2021. "Multiple Attribute Decision-Making Based on Three-Parameter Generalized Weighted Heronian Mean," Mathematics, MDPI, vol. 9(12), pages 1-29, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1363-:d:573913
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    References listed on IDEAS

    as
    1. Xiaodi Liu & Jianjun Zhu & Guodong Liu & Jingjing Hao, 2013. "A Multiple Attribute Decision Making Method Based on Uncertain Linguistic Heronian Mean," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-11, September.
    2. Runtong Zhang & Jun Wang & Xiaomin Zhu & Meimei Xia & Ming Yu, 2017. "Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making," Complexity, Hindawi, vol. 2017, pages 1-16, August.
    3. Peide Liu & Peng Wang, 2017. "Some Improved Linguistic Intuitionistic Fuzzy Aggregation Operators and Their Applications to Multiple-Attribute Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 817-850, May.
    4. Shenqing Jiang & Wei He & Fangfang Qin & Qingqing Cheng, 2020. "Multiple Attribute Group Decision-Making Based on Power Heronian Aggregation Operators under Interval-Valued Dual Hesitant Fuzzy Environment," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-19, June.
    5. Jun Wang & Runtong Zhang & Xiaomin Zhu & Yuping Xing & Borut Buchmeister, 2018. "Some Hesitant Fuzzy Linguistic Muirhead Means with Their Application to Multiattribute Group Decision-Making," Complexity, Hindawi, vol. 2018, pages 1-16, June.
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    Cited by:

    1. Hanshan Li & Yun Hao & Xiaoqian Zhang, 2022. "Numerical Calculation Method of Target Damage Effectiveness Evaluation under Uncertain Information of Warhead Fragments," Mathematics, MDPI, vol. 10(10), pages 1-14, May.

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