A Multiple Attribute Group Decision-making Method Based on the Partitioned Bonferroni Mean of Linguistic Intuitionistic Fuzzy Numbers

  • Peide LiuEmail author
  • Junlin Liu


As a more effective linguistic information representation model, the linguistic intuitionistic fuzzy number (LIFN), made up of the linguistic membership degree (LMD) and the linguistic non-membership degree (LNMD), plays an important role in describing uncertain-decision information in cognitive activity. The partitioned Bonferroni mean (PBM) operator is constructed based on real conditions, considering that some factors considered by decision-makers are interrelated and some are independent. The PBM operator can aggregate evaluation information under various attributes, which are divided into several independent groups; the factors interact with each other within the same group, but the factors are independent of each other when located in different groups. The classical PBM operators and their extensions can handle many decision-making problems but are unable to handle decision-making problems under a linguistic intuitionistic environment. To take full advantage of the PBM operator and LIFNs, this paper combines the PBM operator with LIFNs to propose several PBM operators for aggregating LIFNs. First, the relative theories about LIFNs are reviewed in brief. Then, linguistic intuitionistic fuzzy partitioned BM aggregation operators and partitioned geometric BM aggregation operators are discussed, including the linguistic intuitionistic fuzzy partitioned Bonferroni mean (LIFPBM) operator, the linguistic intuitionistic fuzzy weighted partitioned Bonferroni mean (LIFWPBM) operator, the linguistic intuitionistic fuzzy partitioned geometric Bonferroni mean (LIFPGBM) operator, and the linguistic intuitionistic fuzzy weighted partitioned geometric Bonferroni mean (LIFWPGBM) operator. Moreover, a novel method constructed on the developed operators is presented to address multiple attribute group decision-making (MAGDM) problems with the LIFNs. The feasibility of the proposed method is given by a numeric example, and the comparative analysis of our proposed method and other methods shows some advantages of these new methods. The developed method is constructed based on LIFNs and the PBM operator, and it is more practical and general than other existing methods and easily describes qualitative information that stems from a decision maker’s cognition. In addition, it can more effectively handle the complex relationship among multiple attributes in MAGDM problems.


Partition Bonferroni mean operator Linguistic intuitionistic fuzzy sets MAGDM 


Funding information

This paper is supported by the National Natural Science Foundation of China (Nos. 71771140, 71471172), 文化名家暨“四个一批”人才项目(the Project of cultural masters and “the four kinds of a batch” talents), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045).

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

Research Involving Human Participants and/or Animals

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


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Management Science and EngineeringShandong University of Finance and EconomicsJinanChina

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