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On consistency and priority weights for interval probabilistic linguistic preference relations

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  • Xiangqian Feng

    (Nanjing Normal University)

  • Xiaodong Pang

    (Nanjing Normal University)

  • Lan Zhang

    (Nanjing Normal University)

Abstract

When expressing preferences with different probability weights for different linguistic terms, only partial assessment information is usually to be provided. Then the probability information can be normalized to the interval probability, hence, using interval probabilistic linguistic term sets (IPLTs) is more appropriate. Considering this situation, interval probabilistic linguistic preference relation (IPLPR) is proposed. To measure the consistency of IPLPR, the consistency definition of IPLPR is put forward. For the consistent IPLPR, from which an expected consistent PLPR can be obtained, we can obtain interval weights as the final priorities by using the pairs of linear programming models. We also create the probabilistic linguistic geometric consistency index (PLGCI) of PLPRs to judge whether the IPLPR is satisfactorily consistent. For an unsatisfied consistency IPLPR, the adjusting algorithm is proposed. Probability information is firstly considered to be adjusted. If it is not possible to achieve satisfactory consistency through the adjustment of probability information, then the linguistic terms will be adjusted. In addition to examples of different situations, such as the consistency, satisfactory consistency and consistency improvement, the application example is also given to show the practicability of the proposed methods.

Suggested Citation

  • Xiangqian Feng & Xiaodong Pang & Lan Zhang, 2020. "On consistency and priority weights for interval probabilistic linguistic preference relations," Fuzzy Optimization and Decision Making, Springer, vol. 19(4), pages 529-560, December.
    • Handle: RePEc:spr:fuzodm:v:19:y:2020:i:4:d:10.1007_s10700-020-09328-7
    DOI: 10.1007/s10700-020-09328-7
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    References listed on IDEAS

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    1. Aguaron, Juan & Moreno-Jimenez, Jose Maria, 2003. "The geometric consistency index: Approximated thresholds," European Journal of Operational Research, Elsevier, vol. 147(1), pages 137-145, May.
    2. 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.
    3. Xiao Fang Zhang & Ze Shui Xu & Pei Jia Ren, 2019. "A Novel Hybrid Correlation Measure for Probabilistic Linguistic Term Sets and Crisp Numbers and Its Application in Customer Relationship Management," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 673-694, March.
    4. Huchang Liao & Xiaomei Mi & Zeshui Xu, 2020. "A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 81-134, March.
    5. Mingwei Lin & Zeshui Xu & Yuling Zhai & Zhiqiang Yao, 2018. "Multi-attribute group decision-making under probabilistic uncertain linguistic environment," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(2), pages 157-170, February.
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    Cited by:

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