An interval-valued Pythagorean prioritized operator-based game theoretical framework with its applications in multicriteria group decision making

  • Yuzhen Han
  • Yong DengEmail author
  • Zehong CaoEmail author
  • Chin-Teng Lin
Soft Computing Techniques: Applications and Challenges


Multicriteria decision-making process explicitly evaluates multiple conflicting criteria in decision making. The conventional decision-making approaches assumed that each agent is independent, but the reality is that each agent aims to maximize personal benefit which causes a negative influence on other agents’ behaviors in a real-world competitive environment. In our study, we proposed an interval-valued Pythagorean prioritized operator-based game theoretical framework to mitigate the cross-influence problem. The proposed framework considers both prioritized levels among various criteria and decision makers within five stages. Notably, the interval-valued Pythagorean fuzzy sets are supposed to express the uncertainty of experts, and the game theories are applied to optimize the combination of strategies in interactive situations. Additionally, we also provided illustrative examples to address the application of our proposed framework. In summary, we provided a human-inspired framework to represent the behavior of group decision making in the interactive environment, which is potential to simulate the process of realistic humans thinking.


Interval-valued Pythagorean fuzzy sets Game theory Multicriteria group decision making Priority level 



The authors are grateful to anonymous reviewers for their useful comments and suggestions on improving this paper.


The work is partially supported by National Natural Science Foundation of China (Grant Nos. 61573290, 61503237) and National Undergraduate Training Program for Innovation and Entrepreneurship (Grant No. 201810635012).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights statement

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 London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Fundamental and Frontier ScienceUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.School of Computer and Information ScienceSouthwest UniversityChongqingChina
  3. 3.Faculty of Engineering and IT, Centre for Artificial IntelligenceUniversity of Technology SydneySydneyAustralia
  4. 4.Discipline of ICT, School of Technology, Environments and DesignUniversity of TasmaniaHobartAustralia

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