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Some new basic operations of probabilistic linguistic term sets and their application in multi-criteria decision making

  • Na Yue
  • Jialiang XieEmail author
  • Shuili Chen
Methodologies and Application
  • 40 Downloads

Abstract

This paper is concerned with the operations and methods to tackle the probabilistic linguistic multi-criteria decision making (PL-MCDM) problems where criteria are interactive. To avoid the defects of the existing operations of the probabilistic linguistic term sets (PLTSs) and make the operations easier, we redefine a family of operations for PLTSs and investigate their properties in-depth. Then, based on the probabilistic linguistic group utility measure, the probabilistic linguistic individual regret measure and the probabilistic linguistic compromise measure proposed in this paper, the probabilistic linguistic E-VIKOR method is developed. To make up for the deficiency of the above method, the improved probabilistic linguistic VIKOR method which can not only consider the distances between the alternatives and the positive ideal solution but also consider the distances between the alternatives and the negative ideal solution is developed to solve the correlative PL-MCDM problems. And then a case about the video recommender system is conducted to demonstrate the applicability and effectiveness of the proposed methods. Finally, the improved probabilistic linguistic VIKOR method is compared with the probabilistic linguistic E-VIKOR method, the general VIKOR method and the extended TOPSIS method to show its merits.

Keywords

Probabilistic linguistic term set Operations Shapley value Probabilistic linguistic E-VIKOR method Improved probabilistic linguistic VIKOR method 

Notes

Acknowledgements

We would like to thank Professor Zhenyuan Wang at the University of Nebraska at Omaha for his support and help, and the editors and the anonymous referees for their professional comments which improved the quality of the manuscript. This work is supported in part by the National Natural Science Foundation of China (No. 11371130), the Natural Science Foundation of Fujian Province (No. 2017J01558), Soft science research program of Fujian Province (No. B19085), Key Laboratory of Applied Mathematics of Fujian Province University (Putian University) (No. SX201906) and Pre-Research Fund of Jimei University.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this work.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.College of ScienceJimei UniversityXiamenChina
  2. 2.Chengyi Institute of Applied TechnologyJimei UniversityXiamenChina

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