Advertisement

Fuzzy Sets for Modeling Interstate Conflict

  • Tshilidzi Marwala
  • Monica Lagazio
Chapter
Part of the Advanced Information and Knowledge Processing book series (AI&KP)

Abstract

This chapter investigates the level of transparency of the Takagi-Sugeno neuro-fuzzy model and the support vector machines model by applying them to conflict management, an application which is concerned with causal interpretations of results. The data set used in this investigation is the militarized interstate disputes dataset obtained from the Correlates of War (COW) project. In this chapter, a support vector machine model is trained to predict conflict. Knowledge from the Takagi-Sugeno neuro-fuzzy model is extracted by interpreting the model’s fuzzy rules and their outcomes. It is found that the Takagi-Sugeno neuro-fuzzy model offers some transparency which helps in understanding conflict management. The Takagi-Sugeno neuro-fuzzy model was compared to the support vector machine model and it was found that even though the support vector machine shows marginal advantage over the Takagi-Sugeno neuro-fuzzy model in terms of predictive capacity, the Takagi-Sugeno neuro-fuzzy model allows for linguistics interpretation.

Keywords

Support Vector Machine Membership Function Fuzzy Rule Fuzzy Inference System Support Vector Machine Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Abiyev, R.H., Kaynak, O., Alshanableh, T., Mamedov, F.: A type-2 neuro-fuzzy system based on clustering and gradient techniques applied to system identification and channel equalization. Appl. Soft Comput. 11, 1396–1406 (2011)CrossRefGoogle Scholar
  2. Araujo, E.: Improved Takagi-Sugeno fuzzy approach. In: Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 1154–1158, Hong Kong (2008)Google Scholar
  3. Ata, R., Kocyigit, Y.: An adaptive neuro-fuzzy inference system approach for prediction of tip speed ratio in wind turbines. Expert Syst. Appl. 37, 5454–5460 (2010)CrossRefGoogle Scholar
  4. Babuska, R.: Fuzzy modeling and identification. Ph.D. thesis, Technical University of Delft, Delft (1991)Google Scholar
  5. Babuska, R., Verbruggen, H.: Neuro-fuzzy methods for nonlinear system identification. Annu. Rev. Control 27, 73–85 (2003)CrossRefGoogle Scholar
  6. Barbieri, K.: Economic interdependence – a path to peace or a source of interstate conflict. J. Peace Res. 33, 29–49 (1996)CrossRefGoogle Scholar
  7. Beck, N., Katz, J., Tucker, R.: Taking time seriously: time-series cross-section analysis with a binary dependent variable. Am. J. Polit. Sci. 42, 1260–1288 (1998)CrossRefGoogle Scholar
  8. Beck, N., King, G., Zeng, L.: Improving quantitative studies of international conflict: a conjecture. Am. Polit. Sci. Rev. 94, 21–35 (2000)CrossRefGoogle Scholar
  9. Biacino, L., Gerla, G.: Fuzzy logic, continuity and effectiveness. Arch. Math. Log. 41, 643–667 (2002)MathSciNetMATHCrossRefGoogle Scholar
  10. Bih, J.: Paradigm shift – an introduction to fuzzy logic. IEEE Potential. 25(1), 6–21 (2006)CrossRefGoogle Scholar
  11. Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)Google Scholar
  12. Cabalar, A.F., Cevik, A., Gokceoglu, C., Baykal, G.: Neuro-fuzzy based constitutive modeling of undrained response of Leighton Buzzard Sand mixtures. Expert Syst. Appl. 37, 842–851 (2010)CrossRefGoogle Scholar
  13. Cano-Izquierdo, J., Almonacid, M., Ibarrola, J.J.: Applying neuro-fuzzy model dFasArt in control systems. Eng. Appl. Artif. Intell. 23, 1053–1063 (2010)CrossRefGoogle Scholar
  14. Cantor, G.: Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen. Crelle. J. F. Math. 77, 258–262 (1874)CrossRefGoogle Scholar
  15. Cetisli, B.: Development of an adaptive neuro-fuzzy classifier using linguistic hedges: part 1. Expert Syst. Appl. 37, 6093–6101 (2010)CrossRefGoogle Scholar
  16. Cox, E.: The Fuzzy Systems Handbook: A Practitioner’s Guide to Building, Using, Maintaining Fuzzy Systems. AP Professional, Boston (1994)Google Scholar
  17. Demirli, K., Khoshnejad, M.: Autonomous parallel parking of a car-like mobile robot by a neuro-fuzzy sensor-based controller. Fuzzy Set. Syst. 160, 2876–2891 (2009)MathSciNetCrossRefGoogle Scholar
  18. Devlin, K.: The Joy of Sets. Springer, Berlin (1993)MATHCrossRefGoogle Scholar
  19. El-Sebakhy, E.A.: Flow regimes identification and liquid-holdup prediction in horizontal multiphase flow based on neuro-fuzzy inference systems. Math. Comp. Simulat. 80, 1854–1866 (2010)MathSciNetMATHCrossRefGoogle Scholar
  20. Ferreirós, J.: Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics. Birkhäuser, Basel (1999)MATHGoogle Scholar
  21. Habtemariam, E.A., Marwala, T.: Artificial intelligence for conflict management. In: Proceedings of the IEEE International Joint Conference on Neural Networks, pp. 2583–2588, Montreal (2005)Google Scholar
  22. Hagiwara, H., Mita, A.: Structural health monitoring system using support vector machine. Adv. Build. Technol. 28, 481–488 (2002)CrossRefGoogle Scholar
  23. Hájek, P.: Fuzzy logic and arithmetical hierarchy. Fuzzy Set. Syst. 3, 359–363 (1995)CrossRefGoogle Scholar
  24. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)MATHCrossRefGoogle Scholar
  25. Halpern, J.Y.: Reasoning About Uncertainty. MIT Press, Cambridge (2003)MATHGoogle Scholar
  26. Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice Hall, Englewood Cliffs (1999)MATHGoogle Scholar
  27. Hsu, Y.-C., Lin, S.-F.: Reinforcement group cooperation-based symbiotic evolution for recurrent wavelet-based neuro-fuzzy systems. J. Neurocomput. 72, 2418–2432 (2009)CrossRefGoogle Scholar
  28. Huang, T.M., Kecman, V.: Gene extraction for cancer diagnosis by support vector machines – an improvement. Artif. Intell. Med. 35, 185–194 (2005)CrossRefGoogle Scholar
  29. Hurtado, J.E.: Relevance of support vector machines for stochastic mechanics. Comput. Fluid. Solid. Mech. 20, 2298–2301 (2003)CrossRefGoogle Scholar
  30. Iplikci, S.: Support vector machines based neuro-fuzzy control of nonlinear systems. J. Neurocomput. 73, 2097–2107 (2010)CrossRefGoogle Scholar
  31. Jang, J.-S.R.: ANFIS: Adaptive-network-based Fuzzy Inference System. IEEE Trans. Syst. Man Cybern. 23, 665–685 (1993)CrossRefGoogle Scholar
  32. Jang, J.S.R., Sun, C.T., Mizutani, E.: Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence. Prentice Hall, Toronto (1997)Google Scholar
  33. Johnson, P.: A History of Set Theory. Prindle, Weber & Schmidt, Boston (1972)MATHGoogle Scholar
  34. Jones, D., Bremer, S., Singer, J.: Militarized interstate disputes, 1816–1992 rationale, coding rules and empirical patterns. Conflict Manag. Peace Sci. 15, 585–615 (1996)Google Scholar
  35. Khajeh, A., Modarress, H.: Prediction of solubility of gases in polystyrene by adaptive neuro-fuzzy inference system and radial basis function neural network. Expert Syst. Appl 37, 3070–3074 (2010)CrossRefGoogle Scholar
  36. Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs (1988)MATHGoogle Scholar
  37. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River (1995)MATHGoogle Scholar
  38. Klir, G.J., St Clair, U.H., Yuan, B.: Fuzzy Set Theory: Foundations and Applications. Prentice Hall, Upper Saddle River (1997)MATHGoogle Scholar
  39. Kosko, B.: Fuzzy Thinking: The New Science of Fuzzy Logic. Hyperion, New York (1993)Google Scholar
  40. Kosko, B., Isaka, S.: Fuzzy logic. Sci. Am. 269, 76–81 (1993)CrossRefGoogle Scholar
  41. Kucuk, K., Aksoy, C.O., Basarir, H., Onargan, T., Genis, M., Ozacar, V.: Prediction of the performance of impact hammer by adaptive neuro-fuzzy inference system modelling. Tunn. Undergr. Sp. Tech. 26, 38–45 (2011)CrossRefGoogle Scholar
  42. Kurtulus, B., Razack, M.: Modeling daily discharge responses of a large karstic aquifer using soft computing methods: artificial neural network and neuro-fuzzy. J. Hydrol. 381, 10–111 (2010)CrossRefGoogle Scholar
  43. Kwong, C.K., Wong, T.C., Chan, K.Y.: A methodology of generating customer satisfaction models for new product development using a neuro-fuzzy approach. Expert Syst. Appl 36, 11262–11270 (2009)CrossRefGoogle Scholar
  44. Lagazio, M., Russett, B.: A Neural Network Analysis of MIDs, 1885–1992: Are the Patterns Stable? In the Scourge of War: New Extensions on an Old Problem, ch. Towards a Scientific Understanding of War: Studies in Honor of J. David Singer. University of Michigan Press, Ann Arbor (2004)Google Scholar
  45. Leke, B., Marwala, T., Tettey, T.: Using inverse neural network for HIV adaptive control. Intl. J. Comput. Intell. Res. 3, 11–15 (2007)Google Scholar
  46. Lo, S.: Web service quality control based on text mining using support vector machine. Expert Syst. Appl. 34, 603–610 (2008)CrossRefGoogle Scholar
  47. Mamdani, E.H.: Application of fuzzy algorithms for the control of a dynamic plant. Proc. IEEE. 121, 1585–1588 (1974)Google Scholar
  48. Mansfield, E.D., Snyder, J.: A tale of two democratic peace critiques: a reply to Thompson and Tucker. J. Confl. Res. 41, 457–461 (1997)CrossRefGoogle Scholar
  49. Marwala, T.: Computational Intelligence for Modelling Complex Systems. Research India Publications, Delhi (2007)Google Scholar
  50. Marwala, T.: Computational Intelligence for Missing Data Imputation, Estimation and Management, Knowledge Optimization Techniques. IGI Global Publications, New York (2009)CrossRefGoogle Scholar
  51. Marwala, T., Lagazio, M.: Modelling and controlling interstate conflict. In: Proceedings of the IEEE International Joint Conference on Neural Networks, pp. 1233–1238, Budapest (2004)Google Scholar
  52. Marwala, T., Chakraverty, S., Mahola, U.: Fault classification using multi-layer perceptrons and support vector machines. Intl. J. Eng. Simul. 7, 29–35 (2006)Google Scholar
  53. Mashrei, M.A., Abdulrazzaq, N., Abdalla, T.Y., Rahman, M.S.: Neural networks model and adaptive neuro-fuzzy inference system for predicting the moment capacity of ferrocement members. Eng. Struct. 32, 1723–1734 (2010)CrossRefGoogle Scholar
  54. Min, J.H., Lee, Y.-C.: Bankruptcy prediction using support vector machine with optimal choice of kernel function parameters. Expert Syst. Appl. 28, 603–614 (2005)CrossRefGoogle Scholar
  55. Mitra, P., Shankar, B.U., Pal, S.K.: Segmentation of multispectral remote sensing images using active support vector machines. Pattern Recogn. Lett. 25, 1067–1074 (2004)CrossRefGoogle Scholar
  56. Montazer, G.A., Saremi, H.Q., Khatibi, V.: A neuro-fuzzy inference engine for farsi numeral characters recognition. Expert Syst. Appl. 37, 6327–6337 (2010)CrossRefGoogle Scholar
  57. Nelwamondo, F.V., Marwala, T., Mahola, U.: Early classifications of bearing faults using hidden Markov models, Gaussian mixture models, mel-frequency cepstral coefficients and fractals. Int. J. Innov. Comput., Info. Control 2, 1281–1299 (2006)Google Scholar
  58. Novák, V.: Fuzzy Sets and Their Applications. Adam Hilger, Bristol (1989)MATHGoogle Scholar
  59. Novák, V.: On fuzzy type theory. Fuzzy Set. Syst. 149, 235–273 (2005)MATHCrossRefGoogle Scholar
  60. Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Dordrecht (1999)MATHCrossRefGoogle Scholar
  61. Oneal, J., Russet, B.: The classical liberals were right: democracy, interdependence and conflict, 1950–1985. Int. Stud. Quart. 41, 267–294 (1997)CrossRefGoogle Scholar
  62. Oneal, J., Russet, B.: Prediction and classification with neural network models. Sociol. Method. Res. 4, 499–524 (1999)Google Scholar
  63. Patel, P.B., Marwala, T.: Forecasting closing price indices using neural networks. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, pp. 2351–2356, Taipei, Taiwan (2006)Google Scholar
  64. Patel, P.B., Marwala, T.: Caller behaviour classification using computational intelligence methods. Int. J. Neural Syst. 20, 87–93 (2010)CrossRefGoogle Scholar
  65. Schölkopf, B., Smola, A.J.: Learning with Kernels. MIT Press, Cambridge (2002)Google Scholar
  66. Sentes, M., Babuska, R., Kaymak, U., van Nauta, L.H.: Similarity measures in fuzzy rule base simplification. IEEE Trans. Syst. Man Cybern. B Cybern. 28, 376–386 (1998)CrossRefGoogle Scholar
  67. Shiri, J., Kisi, O.: Short-term and long-term streamflow forecasting using a wavelet and neuro-fuzzy conjunction model. J. Hydrol. 394, 486–493 (2010)CrossRefGoogle Scholar
  68. Sugeno, M.: Industrial Applications of Fuzzy Control. Elsevier, Amsterdam (1985)Google Scholar
  69. Sugeno, M., Kang, G.: Structure identification of fuzzy model. Fuzzy Set. Syst. 28, 15–33 (1988)MathSciNetMATHCrossRefGoogle Scholar
  70. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985)MATHGoogle Scholar
  71. Talei, A., Hock, L., Chua, C., Quek, C.: A novel application of a neuro-fuzzy computational technique in event-based rainfall-runoff modeling. Expert Syst. Appl. 37, 7456–7468 (2010)CrossRefGoogle Scholar
  72. Tettey, T.: A computational intelligence approach to modelling interstate conflict: Conflict and causal interpretations. MSc thesis, University of the Witwatersrand, Johannesburg (2007)Google Scholar
  73. Tettey, T., Marwala, T.: Controlling interstate conflict using neuro-fuzzy modeling and genetic algorithms. In: Proceedings of the 10th International Conference on Intelligent Engineering Systems, pp. 30–34, London (2006a)Google Scholar
  74. Tettey, T., Marwala, T.: Neuro-fuzzy modeling and fuzzy rule extraction applied to conflict management. Lect. Note. Comp. Sci. 4234, 1087–1094 (2006b)CrossRefGoogle Scholar
  75. Tettey, T., Marwala, T.: Conflict modelling and knowledge extraction using computational intelligence methods. In: Proceedings of the 11th IEEE International Conference on Intelligent Engineering Systems, pp. 161–166, Budapest (2007)Google Scholar
  76. Thompson, W., Tucker, R.: A tale of two democratic peace critiques. J. Confl. Res 41, 428–454 (1997)CrossRefGoogle Scholar
  77. Tripathi, S., Srinivas, V.V., Nanjundiah, R.S.: Downscaling of precipitation for climate change scenarios: a support vector machine approach. J. Hydrol. 330, 621–640 (2006)CrossRefGoogle Scholar
  78. Von Altrock, C.: Fuzzy Logic and NeuroFuzzy Applications Explained. Prentice Hall, Englewood Cliffs (1995)Google Scholar
  79. Wright, S., Marwala, T.: Artificial intelligence techniques for steam generator modelling. arXiv:0811.1711 (2006)
  80. Zadeh, L.A.: Fuzzy sets. Info. Control 8, 338–353 (1965)MathSciNetMATHCrossRefGoogle Scholar
  81. Zemankova-Leech, M.: Fuzzy relational data bases. Ph.D. dissertation, Florida State University, Tallahassee (1983)Google Scholar
  82. Zhou, Q., Chan, C.W., Tontiwachwuthikul, P.: An application of neuro-fuzzy technology for analysis of the CO2 capture process. Fuzzy Set. Syst. 161, 2597–2611 (2010)CrossRefGoogle Scholar
  83. Zimmermann, H.: Fuzzy Set Theory and Its Applications. Kluwer Academic Publishers, Boston (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.University of JohannesburgJohannesburgSouth Africa

Personalised recommendations