IDEAS home Printed from https://ideas.repec.org/a/spr/grdene/v15y2006i6d10.1007_s10726-005-9008-4.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10726-005-9008-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10726-005-9008-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Weber, Martin, 1987. "Decision making with incomplete information," European Journal of Operational Research, Elsevier, vol. 28(1), pages 44-57, January.
    2. Kim, Soung Hie & Ahn, Byeong Seok, 1999. "Interactive group decision making procedure under incomplete information," European Journal of Operational Research, Elsevier, vol. 116(3), pages 498-507, August.
    3. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    4. Koksalan, Murat & Ulu, Canan, 2003. "An interactive approach for placing alternatives in preference classes," European Journal of Operational Research, Elsevier, vol. 144(2), pages 429-439, January.
    5. Kim, Soung Hie & Choi, Sang Hyun & Kim, Jae Kyeong, 1999. "An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach," European Journal of Operational Research, Elsevier, vol. 118(1), pages 139-152, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Zeshui Xu & Xiaoqiang Cai, 2012. "Minimizing Group Discordance Optimization Model for Deriving Expert Weights," Group Decision and Negotiation, Springer, vol. 21(6), pages 863-875, November.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dias, Luis C. & Climaco, Joao N., 2005. "Dealing with imprecise information in group multicriteria decisions: a methodology and a GDSS architecture," European Journal of Operational Research, Elsevier, vol. 160(2), pages 291-307, January.
    2. Mateos, A. & Jimenez, A. & Rios-Insua, S., 2006. "Monte Carlo simulation techniques for group decision making with incomplete information," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1842-1864, November.
    3. Mustajoki, Jyri & Hamalainen, Raimo P. & Lindstedt, Mats R.K., 2006. "Using intervals for global sensitivity and worst-case analyses in multiattribute value trees," European Journal of Operational Research, Elsevier, vol. 174(1), pages 278-292, October.
    4. Fu, Chao & Yang, Shanlin, 2012. "An evidential reasoning based consensus model for multiple attribute group decision analysis problems with interval-valued group consensus requirements," European Journal of Operational Research, Elsevier, vol. 223(1), pages 167-176.
    5. Salo, Ahti A., 1995. "Interactive decision aiding for group decision support," European Journal of Operational Research, Elsevier, vol. 84(1), pages 134-149, July.
    6. Iuliana Carmen Barbacioru, 2014. "Grey Relational Analysis Method For Intuitionistic Fuzzy Multiple Attribute Decision Making," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 0, pages 204-209, May.
    7. Mousseau, Vincent & Figueira, Jose & Dias, Luis & Gomes da Silva, Carlos & Climaco, Joao, 2003. "Resolving inconsistencies among constraints on the parameters of an MCDA model," European Journal of Operational Research, Elsevier, vol. 147(1), pages 72-93, May.
    8. S H Choi & B S Ahn, 2009. "IP-MAGS: an incomplete preference-based multiple attribute group support system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(4), pages 496-505, April.
    9. Tom Pape, 2020. "Value of agreement in decision analysis: Concept, measures and application," Papers 2012.13816, arXiv.org.
    10. João N. Clímaco & Luis C. Dias, 2006. "An Approach to Support Negotiation Processes with Imprecise Information Multicriteria Additive Models," Group Decision and Negotiation, Springer, vol. 15(2), pages 171-184, March.
    11. Contreras, I. & Marmol, A.M., 2007. "A lexicographical compromise method for multiple criteria group decision problems with imprecise information," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1530-1539, September.
    12. Meimei Xia & Jian Chen & Xiao-Jun Zeng, 2018. "Decision Analysis on Choquet Integral-Based Multi-Criteria Decision-Making with Imprecise Information," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 677-704, March.
    13. M. A. Hinojosa & A. M. Mármol, 2011. "Egalitarianism and Utilitarianism in Multiple Criteria Decision Problems with Partial Information," Group Decision and Negotiation, Springer, vol. 20(6), pages 707-724, November.
    14. Fu-Ling Cai & Xiuwu Liao & Kan-Liang Wang, 2012. "An interactive sorting approach based on the assignment examples of multiple decision makers with different priorities," Annals of Operations Research, Springer, vol. 197(1), pages 87-108, August.
    15. Pape, Tom, 2017. "Value of agreement in decision analysis: concept, measures and application," LSE Research Online Documents on Economics 68682, London School of Economics and Political Science, LSE Library.
    16. Kim, Soung Hie & Choi, Sang Hyun & Kim, Jae Kyeong, 1999. "An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach," European Journal of Operational Research, Elsevier, vol. 118(1), pages 139-152, October.
    17. Askoura, Youcef & Billot, Antoine, 2021. "Social decision for a measure society," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    18. Ehud Kalai & Roger B. Myerson, 1977. "Values of Games Without Sidepayments," Discussion Papers 267, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Han, Chang Hee & Kim, Jae Kyeong & Choi, Sang Hyun, 2004. "Prioritizing engineering characteristics in quality function deployment with incomplete information: A linear partial ordering approach," International Journal of Production Economics, Elsevier, vol. 91(3), pages 235-249, October.
    20. Jeffrey T. Macher & John W. Mayo & Olga Ukhaneva & Glenn A. Woroch, 2017. "From universal service to universal connectivity," Journal of Regulatory Economics, Springer, vol. 52(1), pages 77-104, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:grdene:v:15:y:2006:i:6:d:10.1007_s10726-005-9008-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.