IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v67y2016i11d10.1057_jors.2016.28.html
   My bibliography  Save this article

A consistency and consensus-based method to group decision making with interval linguistic preference relations

Author

Listed:
  • Fanyong Meng

    (Central South University)

  • Qingxian An

    (Central South University)

  • Xiaohong Chen

    (Central South University
    Hunan University of Commerce)

Abstract

Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers’ preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure.

Suggested Citation

  • Fanyong Meng & Qingxian An & Xiaohong Chen, 2016. "A consistency and consensus-based method to group decision making with interval linguistic preference relations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(11), pages 1419-1437, November.
  • Handle: RePEc:pal:jorsoc:v:67:y:2016:i:11:d:10.1057_jors.2016.28
    DOI: 10.1057/jors.2016.28
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/jors.2016.28
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1057/jors.2016.28?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. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi, 2008. "On consistency measures of linguistic preference relations," European Journal of Operational Research, Elsevier, vol. 189(2), pages 430-444, September.
    2. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Feng, Bo, 2010. "The OWA-based consensus operator under linguistic representation models using position indexes," European Journal of Operational Research, Elsevier, vol. 203(2), pages 455-463, June.
    3. Liu, Fang & Zhang, Wei-Guo & Zhang, Li-Hua, 2014. "Consistency analysis of triangular fuzzy reciprocal preference relations," European Journal of Operational Research, Elsevier, vol. 235(3), pages 718-726.
    4. Herrera, F. & Herrera-Viedma, E., 2000. "Choice functions and mechanisms for linguistic preference relations," European Journal of Operational Research, Elsevier, vol. 120(1), pages 144-161, January.
    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. Yong Liu & Ting Zhou & Wei-xue Diao & Jinhong Yi, 2022. "A multivariate minimum cost consensus approach for two-level group decision making," OPSEARCH, Springer;Operational Research Society of India, vol. 59(3), pages 839-861, September.
    2. Wenqi Liu & Hengjie Zhang & Haiming Liang & Cong-cong Li & Yucheng Dong, 2022. "Managing Consistency and Consensus Issues in Group Decision-Making with Self-Confident Additive Preference Relations and Without Feedback: A Nonlinear Optimization Method," Group Decision and Negotiation, Springer, vol. 31(1), pages 213-240, February.
    3. Jie Tang & Fanyong Meng & Francisco Javier Cabrerizo & Enrique Herrera-Viedma, 2020. "Group Decision Making with Interval-Valued Intuitionistic Multiplicative Linguistic Preference Relations," Group Decision and Negotiation, Springer, vol. 29(1), pages 169-206, February.
    4. Jie Tang & Qingxian An & Fanyong Meng & Xiaohong Chen, 2017. "A Natural Method for Ranking Objects from Hesitant Fuzzy Preference Relations," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1611-1646, November.
    5. Sha Fan & Hengjie Zhang & Huali Tang, 2019. "A Linguistic Hierarchy Model with Self-Confidence Preference Relations and Its Application in Co-Regulation of Food Safety in China," IJERPH, MDPI, vol. 16(16), pages 1-21, August.
    6. Pei Wang & Xuanhua Xu & Shuai Huang, 2019. "An Improved Consensus-Based Model for Large Group Decision Making Problems Considering Experts with Linguistic Weighted Information," Group Decision and Negotiation, Springer, vol. 28(3), pages 619-640, June.
    7. Zhang, Hengjie & Dong, Yucheng & Chiclana, Francisco & Yu, Shui, 2019. "Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design," European Journal of Operational Research, Elsevier, vol. 275(2), pages 580-598.
    8. Jinpei Liu & Zijie Qiang & Peng Wu & Pengcheng Du, 2023. "Multiple stage optimization driven group decision making method with interval linguistic fuzzy preference relations based on ordinal consistency and DEA cross-efficiency," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 309-336, June.

    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. Yan, Hong-Bin & Ma, Tieju & Huynh, Van-Nam, 2017. "On qualitative multi-attribute group decision making and its consensus measure: A probability based perspective," Omega, Elsevier, vol. 70(C), pages 94-117.
    2. González-Arteaga, T. & Alcantud, J.C.R. & de Andrés Calle, R., 2016. "A cardinal dissensus measure based on the Mahalanobis distance," European Journal of Operational Research, Elsevier, vol. 251(2), pages 575-585.
    3. Fu, Chao & Yang, Shanlin, 2011. "An attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context," European Journal of Operational Research, Elsevier, vol. 212(1), pages 179-189, July.
    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. Wu, Zhibin & Huang, Shuai & Xu, Jiuping, 2019. "Multi-stage optimization models for individual consistency and group consensus with preference relations," European Journal of Operational Research, Elsevier, vol. 275(1), pages 182-194.
    6. Gong, Zaiwu & Zhang, Huanhuan & Forrest, Jeffrey & Li, Lianshui & Xu, Xiaoxia, 2015. "Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual," European Journal of Operational Research, Elsevier, vol. 240(1), pages 183-192.
    7. Sun, Bingzhen & Ma, Weimin, 2015. "An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application," Omega, Elsevier, vol. 51(C), pages 83-92.
    8. Atiq-ur Rehman & Mustanser Hussain & Adeel Farooq & Muhammad Akram, 2019. "Consensus-Based Multi-Person Decision Making with Incomplete Fuzzy Preference Relations Using Product Transitivity," Mathematics, MDPI, vol. 7(2), pages 1-13, February.
    9. Jie Tang & Fanyong Meng & Yongliang Zhang, 2022. "Common probability-based interactive algorithms for group decision making with normalized probability linguistic preference relations," Fuzzy Optimization and Decision Making, Springer, vol. 21(1), pages 99-136, March.
    10. Meng, Fanyong & Tan, Chunqiao & Chen, Xiaohong, 2017. "Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study," Omega, Elsevier, vol. 68(C), pages 17-38.
    11. Zhibin Wu & Jiuping Xu & Zeshui Xu, 2016. "A multiple attribute group decision making framework for the evaluation of lean practices at logistics distribution centers," Annals of Operations Research, Springer, vol. 247(2), pages 735-757, December.
    12. Feifei Jin & Chang Li & Jinpei Liu & Ligang Zhou, 2021. "Distribution Linguistic Fuzzy Group Decision Making Based on Consistency and Consensus Analysis," Mathematics, MDPI, vol. 9(19), pages 1-19, October.
    13. Xu, Zeshui, 2005. "Deviation measures of linguistic preference relations in group decision making," Omega, Elsevier, vol. 33(3), pages 249-254, June.
    14. Meng Fanyong & Tan Chunqiao, 2017. "Distance Measures for Hesitant Intuitionistic Fuzzy Linguistic Sets," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(4), pages 207-224.
    15. Manuel E. SANSALVADOR & José M. BROTONS, 2017. "The Application of OWAs in Expertise Processes: The Development of a Model for the Quantification of Hidden Quality Costs," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(3), pages 73-90.
    16. Meimei Xia & Jian Chen & Juliang Zhang, 2015. "Multi-criteria decision making based on relative measures," Annals of Operations Research, Springer, vol. 229(1), pages 791-811, June.
    17. Mamata Sahu & Anjana Gupta, 2019. "Improving the consistency of incomplete hesitant multiplicative preference relation," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 324-343, March.
    18. Zhang, Bowen & Dong, Yucheng & Zhang, Hengjie & Pedrycz, Witold, 2020. "Consensus mechanism with maximum-return modifications and minimum-cost feedback: A perspective of game theory," European Journal of Operational Research, Elsevier, vol. 287(2), pages 546-559.
    19. Fernandez, Eduardo & Olmedo, Rafael, 2013. "An outranking-based general approach to solving group multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 225(3), pages 497-506.
    20. Jie Tang & Qingxian An & Fanyong Meng & Xiaohong Chen, 2017. "A Natural Method for Ranking Objects from Hesitant Fuzzy Preference Relations," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1611-1646, November.

    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:pal:jorsoc:v:67:y:2016:i:11:d:10.1057_jors.2016.28. 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.palgrave-journals.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.