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A Note on Linguistic Hybrid Arithmetic Averaging Operator in Multiple Attribute Group Decision Making with Linguistic Information

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  • Zeshui Xu

    (Tsinghua University)

Abstract

In this paper, we propose a linguistic hybrid arithmetic averaging (LHAA) operator, which is based on linguistic weighted arithmetic averaging (LWAA) operator and extended ordered weighted averaging (EOWA) operator, and study some desirable properties of the LHAA operator. The LHAA operator can not only reflect the importance degrees of both the given argument and its ordered position, but also relieve the influence of unfair arguments on the decision results by weighting these arguments with small values. Based on the LWAA and LHAA operators, we develop a practical approach to multiple attribute group decision making under linguistic environment. The approach first aggregates the individual linguistic preference values into a collective linguistic preference value for each alternative by using the LWAA and LHAA operators (it is worth pointing out that the aggregation process does not produce any loss of linguistic information), and then orders the collective linguistic preference values to obtain the best alternative(s). Finally, an illustrative example is also given to verify the approach and to demonstrate its feasibility and practicality.

Suggested Citation

  • Zeshui Xu, 2006. "A Note on Linguistic Hybrid Arithmetic Averaging Operator in Multiple Attribute Group Decision Making with Linguistic Information," Group Decision and Negotiation, Springer, vol. 15(6), pages 593-604, November.
    • Handle: RePEc:spr:grdene:v:15:y:2006:i:6:d:10.1007_s10726-005-9008-4
    DOI: 10.1007/s10726-005-9008-4
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    References listed on IDEAS

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    Cited by:

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    2. Zhengmin Liu & Peide Liu, 2017. "Intuitionistic uncertain linguistic partitioned Bonferroni means and their application to multiple attribute decision-making," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(5), pages 1092-1105, April.
    3. Xia Liang & Fei Teng & Yan Sun, 2020. "Multiple Group Decision Making for Selecting Emergency Alternatives: A Novel Method Based on the LDWPA Operator and LD-MABAC," IJERPH, MDPI, vol. 17(8), pages 1-20, April.
    4. Pang, Jifang & Liang, Jiye, 2012. "Evaluation of the results of multi-attribute group decision-making with linguistic information," Omega, Elsevier, vol. 40(3), pages 294-301.
    5. Kedong Yin & Pengyu Wang & Xuemei Li, 2017. "The Multi-Attribute Group Decision-Making Method Based on Interval Grey Trapezoid Fuzzy Linguistic Variables," IJERPH, MDPI, vol. 14(12), pages 1-16, December.
    6. Pankaj Gupta & Mukesh Kumar Mehlawat & Faizan Ahemad, 2023. "Selection of renewable energy sources: a novel VIKOR approach in an intuitionistic fuzzy linguistic environment," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 25(4), pages 3429-3467, April.
    7. Ji Chen & Shouzhen Zeng & Chonghui Zhang, 2018. "An OWA Distance-Based, Single-Valued Neutrosophic Linguistic TOPSIS Approach for Green Supplier Evaluation and Selection in Low-Carbon Supply Chains," IJERPH, MDPI, vol. 15(7), pages 1-15, July.
    8. Bingsheng Liu & Meiqing Fu & Shuibo Zhang & Bin Xue & Qi Zhou & Shiruo Zhang, 2018. "An interval-valued 2-tuple linguistic group decision-making model based on the Choquet integral operator," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(2), pages 407-424, January.
    9. Peide Liu & Xinli You, 2018. "Some linguistic neutrosophic Hamy mean operators and their application to multi-attribute group decision making," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-26, March.
    10. Qian-Yun Tan & Cui-Ping Wei & Qi Liu & Xiang-Qian Feng, 2016. "The Hesitant Fuzzy Linguistic TOPSIS Method Based on Novel Information Measures," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-22, October.
    11. Yinfeng Du & Dun Liu, 2021. "A novel approach to relative importance ratings of customer requirements in QFD based on probabilistic linguistic preferences," Fuzzy Optimization and Decision Making, Springer, vol. 20(3), pages 365-395, September.
    12. Zhang-peng Tian & Jing Wang & Jian-qiang Wang & Hong-yu Zhang, 2017. "Simplified Neutrosophic Linguistic Multi-criteria Group Decision-Making Approach to Green Product Development," Group Decision and Negotiation, Springer, vol. 26(3), pages 597-627, May.
    13. Amir Hosein Mahmoodi & Seyed Jafar Sadjadi & Soheil Sadi-Nezhad & Roya Soltani & Farzad Movahedi Sobhani, 2020. "Linguistic Z-number weighted averaging operators and their application to portfolio selection problem," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-34, January.
    14. Jiefeng Wang & Shouzhen Zeng & Chonghui Zhang, 2020. "Single-Valued Neutrosophic Linguistic Logarithmic Weighted Distance Measures and Their Application to Supplier Selection of Fresh Aquatic Products," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    15. Chen Jing & Wang Zhongxing, 2016. "Multiattribute Decision Making Method Based on Intuitionistic Linguistic Aggregation Operator," Journal of Systems Science and Information, De Gruyter, vol. 4(6), pages 574-586, December.

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