Evidential model for intuitionistic fuzzy multi-attribute group decision making

  • Qiang Fu
  • Yafei SongEmail author
  • Cheng-li Fan
  • Lei Lei
  • Xiaodan Wang
Methodologies and Application


Due to the uncertainty existing in real-world, intuitionistic fuzzy sets (IFSs) are used to model uncertain information in multi-attribute group decision making (MAGDM). The intuitionistic fuzzy MAGDM problems have gained great popularity recently. But, most of the current methods depend on various aggregation operators that may provide unreasonable collective intuitionistic fuzzy values of alternatives to be ranked. To solve such problem, a new method is developed based on evidence theory and IFSs. First, the mathematical relation between IFSs and evidence theory is analyzed, followed by the transformation from intuitionistic fuzzy evaluation information to basic belief assignment in evidence theory. Then, a new intuitionistic fuzzy weighted evidential (IFWE) average operator is introduced based on the operation of evidence discounting and evidence combination rule. We also develop a possibility-based ranking method for intuitionistic fuzzy values (IFVs) to obtain the linear ordering of IFVs. The proposed evidential model uses the IFWE average operator to aggregate the decision matrix and the attribute weight that is given by each decision maker, based on which each decision maker’s aggregated decision matrix can be obtained. Based on the decision matrices of all decision makers and the weights of the decision makers, the aggregated intuitionistic fuzzy value of each alternative can be obtained by the IFWE average operator. Finally, the preference order of all alternatives can be obtained by the possibility-based ranking method. Comparative analysis based on several application examples of MAGDM demonstrates that the proposed method can overcome the drawbacks of existing methods for MAGDM in intuitionistic fuzzy environments.


Intuitionistic fuzzy sets Evidence theory Multi-attribute group decision making Intuitionistic fuzzy aggregation operator 



This work was supported by National Natural Science Foundation of China Under Grant Nos. 61703426, 61273275, 61876189, 61806219 and 61503407, and supported by Young Talent Fund of University Association for Science and Technology in Shaanxi, China, Under Grant No. 20190108.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Air and Missile DefenseAir Force Engineering UniversityXi’anChina

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