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.
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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (No. 11371130), Soft science research program of Fujian Province (No. B19085), the projects of Education Department of Fujian Province (No. JT180263), the open fund of Key Laboratory of Applied Mathematics of Fujian Province University (Putian University) (No. SX201906) and Digital Fujian big data modeling and intelligent computing institute, Pre-Research Fund of Jimei University.
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Yue, N., Wu, D., Xie, J. et al. Probabilistic linguistic multi-criteria decision-making based on double information under imperfect conditions. Fuzzy Optim Decis Making 19, 391–433 (2020). https://doi.org/10.1007/s10700-020-09325-w
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DOI: https://doi.org/10.1007/s10700-020-09325-w