Probabilistic linguistic multi-criteria decision-making based on double information under imperfect conditions
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Probabilistic linguistic multi-criteria decision-making based on double information under imperfect conditions Na Yue1 · Dongrui Wu2 · Jialiang Xie1,3,4 · Shuili Chen5
© Springer Science+Business Media, LLC, part of Springer Nature 2020
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,
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Jialiang Xie [email protected] Na Yue [email protected] Dongrui Wu [email protected] Shuili Chen [email protected]
1
College of Science, Jimei University, Xiamen 361021, China
2
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China
3
Key Laboratory of Applied Mathematics of Fujian Province University, Putian 351100, China
4
Digital Fujian big data modeling and intelligent computing institute, Xiamen 361021, China
5
Chengyi Institute of Applied Technology, Jimei University, Xiamen 361021, China
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N. Yue et al.
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. Keywords Probabilistic linguistic term set · Projection · Normalization model · Decision-making method · Data hiding
1 Introduction Since the probabilistic linguistic term set (PLTS) was put forward by Pang et al. (2016) to preserve all the original linguistic information provided by the decision-makers (DMs), many achievements have been made on PLTSs. These results can be divided into three categories: (1) The basic operations for PLTSs, such as the operational laws (Pang et al. 2016; Gou and Xu 2016; Yue et al. 2020), distance measures (Lin et al. 2019; Lin and Xu 2018), possibility degree formulas (Feng et al. 2019), and probabilistic linguistic preference relations (Gao et al. 2019; Song and Hu 2019). (2) The extension of
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