Advertisement

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
  • 56 Downloads

Abstract

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.

Keywords

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

Notes

Acknowledgements

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

Funding

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.

References

  1. 1.
    Liao H, Xu Z, Zeng XJ, Xu DL (2016) An enhanced consensus reaching process in group decision making with intuitionistic fuzzy preference relations. Inf Sci 329(C):274–286CrossRefGoogle Scholar
  2. 2.
    Zhang X, Mahadevan S (2017) A game theoretic approach to network reliability assessment. IEEE Trans Reliab PP(99):1–18Google Scholar
  3. 3.
    Zhang X, Mahadevan S (2018) A bio-inspired approach to traffic network equilibrium assignment problem. IEEE Trans Cybern 48(4):1304–1315CrossRefGoogle Scholar
  4. 4.
    Kannan D, Khodaverdi R, Olfat L, Jafarian A, Diabat A (2013) Integrated fuzzy multi criteria decision making method and multi-objective programming approach for supplier selection and order allocation in a green supply chain. J Clean Prod 47(9):355–367CrossRefGoogle Scholar
  5. 5.
    Jiang W, Wei B, Liu X, Li XY, Zheng H (2018) Intuitionistic fuzzy power aggregation operator based on entropy and its application in decision making. Int J Intell Syst 33(1):49–67CrossRefGoogle Scholar
  6. 6.
    Cao Z, Lin C-T (2018) Inherent fuzzy entropy for the improvement of eeg complexity evaluation. IEEE Trans Fuzzy Syst 2(26):1032–1035CrossRefGoogle Scholar
  7. 7.
    Sayadi MK, Heydari M, Shahanaghi K (2009) Extension of vikor method for decision making problem with interval numbers. Appl Math Model 33(5):2257–2262MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lin C-T, Ding W, Cao Z (2018) Deep neuro-cognitive co-evolution for fuzzy attribute reduction by quantum leaping PSO with nearest-neighbor memeplexes. IEEE Trans Cybern.  https://doi.org/10.1109/TCYB.2018.2834390 Google Scholar
  9. 9.
    Wu S-L, Zehong JC, Wang Y-K, Huang C-S, King J-T, Chen S-A, Lu S-W, Lin C-T, Liu Y-T, Chuang C-H (2017) Eeg-based brain-computer interfaces: a novel neurotechnology and computational intelligence method. IEEE Syst Man Cybern Mag 3(4):16–26CrossRefGoogle Scholar
  10. 10.
    Liu F, Qin Y, Pedrycz W, Zhang WG (2018) A group decision making model based on an inconsistency index of interval multiplicative reciprocal matrices. Knowl Based Syst 145:67–76CrossRefGoogle Scholar
  11. 11.
    Zeshui X, Yager RR (2012) Dynamic intuitionistic fuzzy multi-attribute decision making. Int J Approx Reason 48(1):246–262zbMATHGoogle Scholar
  12. 12.
    Mousavi SM, Foroozesh N, Gitinavard H, Vahdani B (2018) Solving group decision-making problems in manufacturing systems by an uncertain compromise ranking method. Int J Appl Decis Sci 11(1):55Google Scholar
  13. 13.
    Morente-Molinera JA, Kou G, Peng Y, Torres-Albero C, Herrera-Viedma E (2018) Analysing discussions in social networks using group decision making methods and sentiment analysis. Inf Sci 447:157–168CrossRefGoogle Scholar
  14. 14.
    Kang B, Chhipi-Shrestha G, Deng Y, Mori J, Hewage K, Sadiq R (2017) Development of a predictive model for \(Clostridium~difficile\) infection incidence in hospitals using Gaussian mixture model and Dempster–Shafer theory. Stoch Environ Res Risk Assess 32(6):1743–1758CrossRefGoogle Scholar
  15. 15.
    Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 38(2):325–339MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Zhang L, Ding LY, Wu XG, Skibniewski MJ (2017) An improved Dempster–Shafer approach to construction safety risk perception. Knowl Based Syst 132:30–46CrossRefGoogle Scholar
  17. 17.
    Zhang L, Chen HY, Li HX, Wu XG, Skibniewski MJ (2018) Perceiving interactions and dynamics of safety leadership in construction projects. Saf Sci 106:66–78CrossRefGoogle Scholar
  18. 18.
    Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefzbMATHGoogle Scholar
  19. 19.
    Liang D, Zeshui X, Liu D, Yao W (2018) Method for three-way decisions using ideal topsis solutions at Pythagorean fuzzy information. Inf Sci 435:282–295MathSciNetCrossRefGoogle Scholar
  20. 20.
    Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28(5):436–452CrossRefGoogle Scholar
  21. 21.
    Chen T-Y (2014) A prioritized aggregation operator-based approach to multiple criteria decision making using interval-valued intuitionistic fuzzy sets: a comparative perspective. Inf Sci 281:97–112MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Nash J (1951) Non-cooperative games. Ann Math 54(2):286–295MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Zeshui X (2007) Intuitionistic preference relations and their application in group decision making. Inf Sci Int J 177(11):2363–2379MathSciNetzbMATHGoogle Scholar
  24. 24.
    Yager RR (2008) Prioritized aggregation operators. Int J Approx Reason 48(1):263–274MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Cabrerizo FJ, Morente-Molinera JA, Pedrycz W, Taghavi A, Herrera-Viedma E (2018) Granulating linguistic information in decision making under consensus and consistency. Expert Syst Appl 99:83–92CrossRefGoogle Scholar
  26. 26.
    Li X, Jusup M, Wang Z, Li H, Shi L, Podobnik B, Stanley HE, Havlin S, Boccaletti S (2017) Punishment diminishes the benefits of network reciprocity in social dilemma experiments. Proc Natl Acad Sci 115(1):30–35CrossRefGoogle Scholar
  27. 27.
    Wang Z, Xia C-Y, Meloni S, Zhou C-S, Moreno Y (2013) Impact of social punishment on cooperative behavior in complex networks. Sci Rep 3:3055CrossRefGoogle Scholar
  28. 28.
    Wang Z, Andrews MA, Wu Z-X, Wang L, Bauch CT (2015) Coupled disease–behavior dynamics on complex networks: a review. Phys Life Rev 15:1–29CrossRefGoogle Scholar
  29. 29.
    Deng XY, Zhang ZP, Deng Y, Liu Q, Chang S (2016) Self-adaptive win-stay-lose-shift reference selection mechanism promotes cooperation on a square lattice. Appl Math Comput 284:322–331MathSciNetGoogle Scholar
  30. 30.
    Nash JF (1950) Equilibrium points in \(n\)-person games. Proc Natl Acad Sci USA 36(1):48MathSciNetCrossRefzbMATHGoogle Scholar

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

Personalised recommendations