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Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

Author

Listed:
  • Runtong Zhang
  • Jun Wang
  • Xiaomin Zhu
  • Meimei Xia
  • Ming Yu

Abstract

The Pythagorean fuzzy set as an extension of the intuitionistic fuzzy set characterized by membership and nonmembership degrees has been introduced recently. Accordingly, the square sum of the membership and nonmembership degrees is a maximum of one. The Pythagorean fuzzy set has been previously applied to multiattribute group decision-making. This study develops a few aggregation operators for fusing the Pythagorean fuzzy information, and a novel approach to decision-making is introduced based on the proposed operators. First, we extend the generalized Bonferroni mean to the Pythagorean fuzzy environment and introduce the generalized Pythagorean fuzzy Bonferroni mean and the generalized Pythagorean fuzzy Bonferroni geometric mean. Second, a new generalization of the Bonferroni mean, namely, the dual generalized Bonferroni mean, is proposed by considering the shortcomings of the generalized Bonferroni mean. Furthermore, we investigate the dual generalized Bonferroni mean in the Pythagorean fuzzy sets and introduce the dual generalized Pythagorean fuzzy Bonferroni mean and dual generalized Pythagorean fuzzy Bonferroni geometric mean. Third, a novel approach to multiattribute group decision-making based on proposed operators is proposed. Lastly, a numerical instance is provided to illustrate the validity of the new approach.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:5937376
    DOI: 10.1155/2017/5937376
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    References listed on IDEAS

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    1. Zeshui Xu & Hui Hu, 2010. "Projection Models For Intuitionistic Fuzzy Multiple Attribute Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 267-280.
    2. Zeshui Xu, 2010. "A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making," Group Decision and Negotiation, Springer, vol. 19(1), pages 57-76, January.
    3. Dejian Yu, 2015. "A scientometrics review on aggregation operator research," Scientometrics, Springer;Akadémiai Kiadó, vol. 105(1), pages 115-133, October.
    4. B Zhu & Z S Xu, 2013. "Hesitant fuzzy Bonferroni means for multi-criteria decision making," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(12), pages 1831-1840, December.
    5. Peide Liu & Lili Zhang & Xi Liu & Peng Wang, 2016. "Multi-Valued Neutrosophic Number Bonferroni Mean Operators with their Applications in Multiple Attribute Group Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1181-1210, September.
    6. Shouzhen Zeng & Jianping Chen & Xingsen Li, 2016. "A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 403-422, March.
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    Cited by:

    1. Miin-Shen Yang & Zahid Hussain, 2018. "Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making," Complexity, Hindawi, vol. 2018, pages 1-14, November.
    2. Mingwei Lin & Jiuhan Wei & Zeshui Xu & Riqing Chen, 2018. "Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators," Complexity, Hindawi, vol. 2018, pages 1-24, November.
    3. 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.
    4. Yuchu Qin & Xiaolan Cui & Meifa Huang & Yanru Zhong & Zhemin Tang & Peizhi Shi, 2019. "Archimedean Muirhead Aggregation Operators of q-Rung Orthopair Fuzzy Numbers for Multicriteria Group Decision Making," Complexity, Hindawi, vol. 2019, pages 1-33, December.
    5. Zaoli Yang & Xin Li & Zehong Cao & Jinqiu Li, 2019. "Q-rung Orthopair Normal Fuzzy Aggregation Operators and Their Application in Multi-Attribute Decision-Making," Mathematics, MDPI, vol. 7(12), pages 1-26, November.
    6. Huijuan Wang & Xin Wang & Lidong Wang, 2019. "Multicriteria Decision Making Based on Archimedean Bonferroni Mean Operators of Hesitant Fermatean 2-Tuple Linguistic Terms," Complexity, Hindawi, vol. 2019, pages 1-19, December.

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