International Journal of Fuzzy Systems

, Volume 20, Issue 3, pp 958–969 | Cite as

On Novel Operational Laws and Aggregation Operators of Picture 2-Tuple Linguistic Information for MCDM Problems

  • Xue-yang Zhang
  • Jian-qiang WangEmail author
  • Jun-hua Hu


This paper primarily focuses on multi-criteria decision-making (MCDM) based on picture 2-tuple linguistic information. Since the picture 2-tuple linguistic set is structured by a linguistic 2-tuple and a picture fuzzy set, we first point out the inappropriateness of existing operations relating to picture fuzzy numbers and picture 2-tuple linguistic numbers. For the purpose of improving these misleading computations, we further propose novel operational laws for picture 2-tuple linguistic numbers from a correct version. Counterexamples, which are in one-to-one correspondence with the listed counterintuitive cases, are furnished to illustrate the limitations of existing operations and prove the feasibility of our newly presented operations. Moreover, by applying the novel operations, we put forward some modified aggregation operators which are further employed to a handling method for the MCDM problem with a picture 2-tuple linguistic matrix. Finally, two comparative and illustrative examples are furnished to verify the applicability and advantages of the proposed method.


Picture 2-tuple linguistic set Inappropriateness Novel operational laws Multi-criteria decision-making Modified aggregation operator 



The authors would like to sincerely thank the editors and three anonymous reviewers for their constructive and valuable suggestions. This work was supported by the National Natural Science Foundation of China (No. 71571193).

Compliance with Ethical Standards

Conflict of interest

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


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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of BusinessCentral South UniversityChangshaPeople’s Republic of China

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