Advertisement

Theory and Implementation of Sensitivity Analyses Based on Their Algebraic Representation in the Graph Model

  • Jinshuai Zhao
  • Haiyan XuEmail author
  • Keith W. Hipel
  • Baohua Yang
Article
  • 5 Downloads

Abstract

Sensitivity analyses based on an algebraic representation in the graph model for conflict resolution (GMCR) are generalized for ascertaining the robustness of stability results by varying decision makers’ preference ranking. The ordinal preferences in GMCR are advantageous to carry out sensitivity analyses with respect to systematically identifying the influence of preference alterations upon the four basic stabilities consisting of Nash stability, general metarationality, symmetric metarationality and sequential stability. The proposed algebraic representation of the four basic stabilities is not only effective and convenient for computer implementation of sensitivity analysis, but also makes it easier to understand the meaning of the four stabilities when compared with the existing matrix representation. Further, these sensitivity analyses results are embedded into the latest version of the decision support system NUAAGMCR, which can be used to study real-world conflicts. To illustrate how these contributions to sensitivity analyses can be applied in practice and provide valuable strategic insights, they are used to investigate the civil war conflict in South Sudan.

Keywords

Sensitivity analyses algebraic expression graph model ordinal preference conflict resolution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

The authors would like to express their appreciation to the anonymous reviewers and Editor for their constructive comments which improved the quality of the paper. The authors are grateful for the financial support supplied by the National Natural Science Foundation of China (71471087, 71071076 and 61673209), a Discovery Grant from the National Sciences and Engineering Research Council of Canada, and the Ministry of Education Humanities and Social Science Planning Foundation of China (18YJA630128).

References

  1. Bashar MA, Hipel KW, Kilgour DM (2012). Fuzzy preferences in the graph model for conflict resolution. IEEE Transactions on Fuzzy Systems 20(4):760–770.CrossRefGoogle Scholar
  2. Bashar MA, Hipel KW, Kilgour DM, Obeidi A (2017). Interval fuzzy preferences in the graph model for conflict resolution. Fuzzy Optimization and Decision Making 17(3):287–315.MathSciNetCrossRefzbMATHGoogle Scholar
  3. Ben-Haim Y, Hipel KW (2002). The graph model for conflict resolution with information-gap uncertainty in preferences. Applied Mathematics and Computation 126(2-3):319–340.MathSciNetCrossRefzbMATHGoogle Scholar
  4. Fang L, Hipel KW, Kilgour DM (1993). Interactive Decision Making: The Graph Model for Conflict Resolution. Wiley, New York.Google Scholar
  5. Fraser NM, Hipel KW (1979). Solving complex conflicts. IEEE Transactions on Systems, Man, and Cybernetics 9(12): 805–817.CrossRefGoogle Scholar
  6. Fraser NM, Hipel KW (1984). Conflict Analysis: Models and Resolutions. Horth-Holland, New York.zbMATHGoogle Scholar
  7. Garcia A, Hipel KW (2017). Inverse engineering preferences in simple games. Applied Mathematics and Computation 311:184–194.MathSciNetCrossRefGoogle Scholar
  8. Hamouda L, Kilgour DM, Hipel KW (2004). Strength of preference in the graph model for conflict resolution. Group Decision and Negotiation 13(5):449–462.CrossRefGoogle Scholar
  9. Hamouda L, Kilgour DM, Hipel KW (2006). Strength of preference in graph models for multiple decision maker conflicts. Applied Mathematics and Computation 179(1):314–327.MathSciNetCrossRefzbMATHGoogle Scholar
  10. Hipel KW, Fang L, Kilgour DM (1990). A formal analysis of the Canada-U.S. softwood lumber dispute. European Journal of Operation Research 46(2): 235–246.CrossRefGoogle Scholar
  11. Howard N (1971). Paradoxes of Rationality: Theory of Metagames and Political Behavior. Cambridge: MIT Press, MA.Google Scholar
  12. Kilgour DM, Hipel KW, Fang L (1987). The graph model for conflicts. Automatica 23(1):41–55.MathSciNetCrossRefzbMATHGoogle Scholar
  13. Kinsara RA, Kilgour DM, Hipel KW (2015). Inverse approach to the graph model for conflict resolution. IEEE Transactions on Systems, Man, and Cybernetics: Systems 45(5):734–742.CrossRefGoogle Scholar
  14. Kuang H, Bashar MA, Hipel KW, Kilgour DM (2015). Grey-based preference in a graph model for conflict resolution with multiple decision makers. IEEE Transactions on Systems, Man, and Cybernetics 45(9):1254–1267.CrossRefGoogle Scholar
  15. Li KW, Hipel KW, Kilgour DW, Fang L (2002). Stability definitions for 2-player conflict models with uncertain preferences. IEEE International Conference on Systems, Man, Cybernetics, Yasmine Hammamet, Tunisia, October 0609, 2002.Google Scholar
  16. Li KW, Hipel KW, Kilgour DM, Fang L (2004). Preference uncertainty in the graph model for conflict resolution. IEEE Transactions on Systems, Man, and Cybernetics: Part A 34(4):507–520.CrossRefGoogle Scholar
  17. Li KW, Inohara T, Xu H (2014). Coalition analysis with preference uncertainty in group decision support. Applied Mathematics and Computation 231(1):307–319.MathSciNetCrossRefzbMATHGoogle Scholar
  18. Nash JF (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America 36(1):48–49.MathSciNetCrossRefzbMATHGoogle Scholar
  19. Nash JF (1951). Non-cooperative games. Annals of Mathematics 54(2):286–295.MathSciNetCrossRefzbMATHGoogle Scholar
  20. Pianosi F, Beven K, Freeer J, et al (2016). Sensitivity analysis of environmental models: A systematic review with practical workflow. Environmental Modeling and Software 79:214–232.CrossRefGoogle Scholar
  21. Philpot S, Hipel KW, Johnson P (2016). Strategic analysis of a water rights conflict in the south western United States. Journal of Environmental Management 180(15):247–256.CrossRefGoogle Scholar
  22. Rego LC, dos Santos AM (2015). Probabilistic preferences in the graph model for conflict resolution. IEEE Transactions on Systems, Man, and Cybernetics: Systems 45(4):595–608.CrossRefGoogle Scholar
  23. Sakakibara H, Okada N, Nakase D (2002). The application of robustness analysis to the conflict with incomplete information. IEEE Transactions on Systems, Man, and Cybernetics: Part C 32(1):14–23.CrossRefGoogle Scholar
  24. Von Neumann J, Morgenstern O (1944). Theory of Games and Economic Behavior. Princeton: Princeton University Press, NJ.zbMATHGoogle Scholar
  25. Xu H, Hipel KW, Kilgour DM (2007). Matrix representation of conflicts with two decision-makers. IEEE International Proceedings on Systems, Man, and Cybernetics Montreal, Que. Canada, October 07–10, 2007.Google Scholar
  26. Xu H, Hipel KW, Kilgour DM (2009). Matrix representation of solution concepts in multiple decision maker graph models. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 39(1):96–108.CrossRefGoogle Scholar
  27. Xu H, Hipel KW, Kilgour DM (2009). Multiple levels of preference in interactive strategic decisions. Discrete Applied Mathematics 57(15):3300–3313.MathSciNetCrossRefzbMATHGoogle Scholar
  28. Xu H, Hipel KW, Kilgour DM, Fang L (2018). Conflict Resolution Using the Graph Model: Strategic Interactions in Competition and Cooperation. Springer.CrossRefzbMATHGoogle Scholar
  29. Xu H, Kilgour DM, Hipel KW, Graeme Kemkes (2010). Using matrices to link conflict evolution and resolution in a graph model. European Journal of Operational Research 207(1):318–329.MathSciNetCrossRefzbMATHGoogle Scholar
  30. Xu H, Hipel KW, Kilgour DM, Chen Y (2010). Combining strength and uncertainty for preferences in the graph model for conflict resolution with multiple decision makers. Theory and Decision 69(4): 497–521.MathSciNetCrossRefzbMATHGoogle Scholar
  31. Zhao J, Xu H, Wang J (2017). Sensitivity of conflict analysis based on algebraic expression. Systems Engineering 35(7):153–158 (Chinese Journal).Google Scholar

Copyright information

© Systems Engineering Society of China and Springer-Verlag GmbH Germany 2019

Authors and Affiliations

  • Jinshuai Zhao
    • 1
    • 2
  • Haiyan Xu
    • 1
    Email author
  • Keith W. Hipel
    • 3
  • Baohua Yang
    • 4
  1. 1.College of Economics and ManagementNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.College of Computer Science and TechnologyJiangsu Normal UniversityXuzhouChina
  3. 3.Department of Systems Design EngineeringUniversity of WaterlooWaterlooCanada
  4. 4.School of BusinessJiangsu Normal UniversityXuzhouChina

Personalised recommendations