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The Trapezoidal Fuzzy Two-Dimensional Linguistic Power Generalized Hamy Mean Operator and Its Application in Multi-Attribute Decision-Making

Author

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  • Yisheng Liu

    (School of Economic and Management, Beijing Jiaotong University, Beijing 100044, China)

  • Ye Li

    (School of Economic and Management, Beijing Jiaotong University, Beijing 100044, China)

Abstract

As a common information aggregation tool, the Hamy mean (HM) operator can consider the relationships among multiple input elements, but cannot adjust the effect of elements. In this paper, we integrate the idea of generalized a weighted average (GWA) operator into the HM operator, and reduce the influence of related elements by adjusting the value of the parameter. In addition, considering that extreme input data may lead to a deviation in the results, we further combine the power average (PA) operator with HM, and propose the power generalized Hamy mean (PGHM) operator. Then, we extend the PGHM operator to the trapezoidal fuzzy two-dimensional linguistic environment, and propose two new information aggregation tools, the trapezoidal fuzzy two-dimensional linguistic power generalized Hamy mean (TF2DLPGHM) operator and the weighted TF2DLPGHM (WTF2DLPGHM) operator. Some properties and special cases of these operators are discussed. Furthermore, based on the proposed WTF2DLPGHM operator, a new multi-attribute decision-making method is proposed for lean management evaluation of industrial residential projects. Finally, an example is given to show the specific steps, effectiveness, and superiority of the method.

Suggested Citation

  • Yisheng Liu & Ye Li, 2020. "The Trapezoidal Fuzzy Two-Dimensional Linguistic Power Generalized Hamy Mean Operator and Its Application in Multi-Attribute Decision-Making," Mathematics, MDPI, vol. 8(1), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:122-:d:308307
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    References listed on IDEAS

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    1. Xu, Zeshui, 2005. "Deviation measures of linguistic preference relations in group decision making," Omega, Elsevier, vol. 33(3), pages 249-254, June.
    2. Peide Liu & Li He & Xiaocun Yu, 2016. "Generalized Hybrid Aggregation Operators Based on the 2-Dimension Uncertain Linguistic Information for Multiple Attribute Group Decision Making," Group Decision and Negotiation, Springer, vol. 25(1), pages 103-126, January.
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