Choquet integrals of weighted generalized and group generalized intuitionistic fuzzy soft sets

  • Sheng LiEmail author
  • Xiao-qi Peng
  • Yu-xiao Li


For many real multi-criteria decision-making (MCDM) problems under intuitionistic fuzzy environment, most criteria have interactive characteristics so that it is not suitable for us to aggregate them by traditional aggregation operators based on additive measures. To approximate the human subjective decision-making process, this paper puts forward the new aggregation operators of generalized intuitionistic fuzzy soft set (GIFSS) and group generalized intuitionistic fuzzy soft sets (G-GIFSS) through the Chqouet integral. These new operators not only demonstrate the interaction phenomena among elements, experts (or moderators) or the ordered positions of them, but also consider their importance or the order positions of them. Furthermore, the new operators are not necessary to assume additivity and independence among decision-making criteria. It should be noted that the existing aggregation operators of GIFSS and G-GIFSS are special cases of the new Choquet integral operators. Two Choquet integral operator-based approaches are developed to solve the MCDM under the intuitionistic fuzzy soft set environment. Finally, a practical example of MCDM is given to validate the effectiveness of the proposal.


Choquet integral GIFSS G-GIFSS Aggregation operators Correlations 



This study was funded by National Natural Science Foundation of China (Grant No. 61490702).

Compliance with ethical standards

Conflict of interest

Sheng Li declares that he has no conflict of interest. Xiao-qi Peng declares that she has no conflict of interest. Yu-xiao Li declares that she has no conflict of interest.

Ethical approval

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

Informed consent

Informed consent was obtained from all individual participants included in the study.


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

Authors and Affiliations

  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaChina
  2. 2.School of ScienceJiangxi University of Science and TechnologyGanzhouChina
  3. 3.School of Information Science and EngineeringHunan First Normal UniversityChangshaChina

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