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Probabilistic linguistic multi-criteria decision-making based on double information under imperfect conditions

Author

Listed:
  • Na Yue

    (Jimei University)

  • Dongrui Wu

    (Huazhong University of Science and Technology)

  • Jialiang Xie

    (Jimei University
    Key Laboratory of Applied Mathematics of Fujian Province University
    Digital Fujian big data modeling and intelligent computing institute)

  • Shuili Chen

    (Jimei University)

Abstract

In this paper, we study four projection-based normalization models and a decision-making method for probabilistic linguistic multi-criteria decision-making problems, in which the assessment information about an alternative with respect to a criterion is incomplete and the criteria weight values are not precisely known but the ranges are available. To apply the projection to the probabilistic linguistic environment, we propose the equivalent expression forms of the probabilistic linguistic term sets, and then the equivalent transformation functions between the probabilistic linguistic term set and its associated vector are presented to realize the conversion between the operations on the probabilistic linguistic term sets and the operations on their associated vectors. Next, the projection formulas of the probabilistic linguistic term sets are introduced to build different normalization models for different types of uncertain probabilistic linguistic multi-criteria decision-making problems. After that, a new deviation degree formula is proposed to account for the rationality and validity of the normalization models from the theoretical perspective. Finally, the probabilistic linguistic two-step method is used to determine the criteria weights values and rank the alternatives, and the validity of these projection-based normalization models and our proposed decision-making method are illustrated by a case about the performance assessment of data hiding techniques.

Suggested Citation

  • Na Yue & Dongrui Wu & Jialiang Xie & Shuili Chen, 2020. "Probabilistic linguistic multi-criteria decision-making based on double information under imperfect conditions," Fuzzy Optimization and Decision Making, Springer, vol. 19(4), pages 391-433, December.
    • Handle: RePEc:spr:fuzodm:v:19:y:2020:i:4:d:10.1007_s10700-020-09325-w
    DOI: 10.1007/s10700-020-09325-w
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    References listed on IDEAS

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    1. 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:

    1. Min Xue & Chao Fu & Shanlin Yang, 2022. "A comparative analysis of probabilistic linguistic preference relations and distributed preference relations for decision making," Fuzzy Optimization and Decision Making, Springer, vol. 21(1), pages 71-97, March.

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