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Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making

Author

Listed:
  • Mei Tang

    (School of Business, Sichuan Normal University, Chengdu 610101, China)

  • Jie Wang

    (School of Business, Sichuan Normal University, Chengdu 610101, China)

  • Jianping Lu

    (School of Business, Sichuan Normal University, Chengdu 610101, China)

  • Guiwu Wei

    (School of Business, Sichuan Normal University, Chengdu 610101, China)

  • Cun Wei

    (School of Business, Sichuan Normal University, Chengdu 610101, China
    School of Statistics, Southwestern University of Finance and Economics, Chengdu 611130, China)

  • Yu Wei

    (School of Finance, Yunnan University of Finance and Economics, Kunming 650221, China)

Abstract

On account of the indeterminacy and subjectivity of decision makers (DMs) in complexity decision-making environments, the evaluation information over alternatives presented by DMs is usually fuzzy and ambiguous. As the generalization of intuitionistic fuzzy sets (IFSs), the Pythagorean fuzzy set (PFS) is more useful in expressing fuzzy and ambiguous information. Meanwhile, in order to consider human hesitance, dual hesitant Pythagorean fuzzy sets (DHPFSs) are presented, which can be more valid for handling real multiple attribute decision-making (MADM) problems. To fuse the information in DHPFSs more effectively, in this article, some dual hesitant Pythagorean fuzzy Heronian mean operators, which can consider the relationships between arguments being fused, are defined and studied. Evidently, the new proposed operators can obtain more exact results than other existing methods. In addition, some important properties of these Heronian mean (HM) operators are discussed. Subsequently, the defined aggregation operators are used in MADM with dual hesitant Pythagorean fuzzy numbers (DHPFNs), and the MADM model is developed. In accordance with the defined operators and the built model, the dual hesitant Pythagorean fuzzy generalized weighted Heronian mean (DHPFGWHM) operator and dual hesitant Pythagorean fuzzy generalized geometric weighted Heronian mean (DHPFGGWHM) operator are applied to deal with the green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analyzed by comparing them with some existing approaches. The method presented in this paper can effectively solve the MADM problems in which the decision-making information is expressed by DHPFNs and the attributes are interactive.

Suggested Citation

  • Mei Tang & Jie Wang & Jianping Lu & Guiwu Wei & Cun Wei & Yu Wei, 2019. "Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making," Mathematics, MDPI, vol. 7(4), pages 1-27, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:344-:d:221704
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    References listed on IDEAS

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    1. Jianping Lu & Tingting He & Guiwu Wei & Jiang Wu & Cun Wei, 2020. "Cumulative Prospect Theory: Performance Evaluation of Government Purchases of Home-Based Elderly-Care Services Using the Pythagorean 2-tuple Linguistic TODIM Method," IJERPH, MDPI, vol. 17(6), pages 1-21, March.
    2. Guiwu Wei & Cun Wei & Jiang Wu & Hongjun Wang, 2019. "Supplier Selection of Medical Consumption Products with a Probabilistic Linguistic MABAC Method," IJERPH, MDPI, vol. 16(24), pages 1-15, December.

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