Rough Sets for Modeling Interstate Conflict

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


This chapter applies the rough set technique to model militarized interstate disputes. One aspect of modeling using rough sets is the issue of granulizing the input data. In this chapter, two granulization techniques are introduced, implemented, and compared. These are the equal-width-bin and equal-frequency-bin partitioning techniques. The rough set model is also compared to the neuro-fuzzy model introduced in  Chap. 6. The results obtained demonstrate that equal-width-bin partitioning gives better accuracy than equal-frequency-bin partitioning. However, both techniques were found to give less accurate results than neuro-fuzzy sets. Also, they were found to be more transparent than neuro-rough sets. Furthermore, it is observed that the rules generated from the rough sets are linguistic and easy-to-interpret in comparison with the ones generated from the neuro-fuzzy model.


Recurrent Neural Network Basic Probability Assignment Indiscernibility Relation Rough Membership Function Generalize Radial Basis Function Network 
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.


  1. Araujo, E.: Improved Takagi-Sugeno fuzzy approach. In: IEEE International Conference on Fuzzy Systems, pp. 1154–1158, Hong Kong (2008)Google Scholar
  2. Azadeh, A., Saberi, M., Moghaddam, R.T., Javanmardi, L.: An integrated data envelopment analysis – artificial neural network-rough set algorithm for assessment of personnel efficiency. Expert Syst. Appl. 38, 1364–1373 (2011)CrossRefGoogle Scholar
  3. Babuska, R., Verbruggen, H.: Neuro-fuzzy methods for nonlinear system identification. Annu. Rev. Control. 27, 73–85 (2003)CrossRefGoogle Scholar
  4. Bazan, J., Nguyen, H.S., Szczuka, M.: A view on rough set concept approximations. Fund. Inform. 59, 107–118 (2004)MathSciNetMATHGoogle Scholar
  5. Beynon, M.: Reducts within the variable precision rough sets model: a further investigation. Eur. J. Oper. Res. 134, 592–605 (2001)MATHCrossRefGoogle Scholar
  6. Bi, Y., Anderson, T., McClean, S.: A rough set model with ontologies for discovering maximal association rules in document collections. Knowl. Based Syst. 16, 243–251 (2003)CrossRefGoogle Scholar
  7. Bilski, P.: An unsupervised learning method for comparing the quality of the soft computing algorithms in analog systems diagnostics. Przeglad Elektrotechniczny 86, 242–247 (2010)Google Scholar
  8. Chanas, S., Kuchta, D.: Further remarks on the relation between rough and fuzzy sets. Fuzzy Set. Syst. 47, 391–394 (1992)MathSciNetMATHCrossRefGoogle Scholar
  9. Chen, C., Shen, J., Chen, B., Shang, C.-X., Wang. Y.-C.: Building symptoms diagnosis criteria of traditional Chinese medical science treatment on the elderly’s pneumonia by the rough set theory. In: Proceedings of the 29th Chinese Control Conference, pp. 5268–5271, Beijing (2010)Google Scholar
  10. Chen, R., Zhang, Z., Wu, D., Zhang, P., Zhang, X., Wang, Y., Shi, Y.: Prediction of protein interaction hot spots using rough set-based multiple criteria linear programming. J. Theor. Biol. 269, 174–180 (2011)CrossRefGoogle Scholar
  11. Coulibaly, P., Evora, N.D.: Comparison of neural network methods for infilling missing daily weather records. J. Hydrol. 341, 27–41 (2007)CrossRefGoogle Scholar
  12. Crossingham, B.: Rough set partitioning using computational intelligence approach. MSc thesis, University of the Witwatersrand, Johannesburg (2007)Google Scholar
  13. Crossingham, B., Marwala, T.: Using optimisation techniques to granulise rough set partitions. Comput. Model. Life Sci. 952, 248–257 (2007)Google Scholar
  14. Crossingham, B., Marwala, T.: Using genetic algorithms to optimise rough set partition sizes for HIV data analysis. Stud. Comput. Intell. 78, 245–250 (2008a)CrossRefGoogle Scholar
  15. Crossingham, B., Marwala, T.: Using optimisation techniques for discretizing rough set partitions. Int. J. Hybrid Intell. Syst. 5, 219–236 (2008b)MATHGoogle Scholar
  16. Crossingham, B., Marwala, T., Lagazio, M.: Optimised rough sets for modeling interstate conflict. In: Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp. 1198–1204, Singapore (2008)Google Scholar
  17. Crossingham, B., Marwala, T., Lagazio, M.: Evolutionarily optimized rough set partitions. ICIC Exp. Lett. 3, 241–246 (2009)Google Scholar
  18. Degang, C., Wenxiu, Z., Yeung, D., Tsang, E.C.C.: Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Inf. Sci. 176, 1829–1848 (2006)MathSciNetMATHCrossRefGoogle Scholar
  19. Deng, T., Chen, Y., Xu, W., Dai, Q.: A novel approach to fuzzy rough sets based on a fuzzy covering. Inf. Sci. 177, 2308–2326 (2007)MathSciNetMATHCrossRefGoogle Scholar
  20. Dubois, D.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–209 (1990)MATHCrossRefGoogle Scholar
  21. Fayyad, U., Irani, K.: Multi-interval discretization of continuous valued attributes for classification learning. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence, pp. 1022–1027, Los Alamos (1993)Google Scholar
  22. Goh, C., Law, R.: Incorporating the rough sets theory into travel demand analysis. Tourism Manag. 24, 511–517 (2003)CrossRefGoogle Scholar
  23. Gong, J., Yang, H., Zhong, L.: Case-based reasoning based on rough set in rare-earth extraction process. In: Proceedings of the 29th Chinese Control Conference, pp. 70–1706, Beijing (2010)Google Scholar
  24. Grzymala-Busse, J.W., Hu, M.: A comparison of several approaches to missing attribute values in data mining. Lect. Notes Artif. Intell. 205, 378–385 (2001)Google Scholar
  25. Grzymala-Busse, J.W.: Three approaches to missing attribute values – a rough set perspective. In: Proceedings of the IEEE 4th International Conference on Data Mining, pp. 57–64, Brighton (2004)Google Scholar
  26. Grzymala-Busse, J.W., Siddhaye, S.: Rough set approaches to rule induction from incomplete data. In: Proceedings of the 10th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, vol. 2, pp. 923–930, Perugia (2004)Google Scholar
  27. Hoa, N.S., Son, N.H.: Rough set approach to approximation of concepts from taxonomy. (2008)
  28. Huang, C.-C., Liang, W.-Y., Shian-Hua, L., Tseng, T.-L., Chiang, H.-Y.: A rough set based approach to patent development with the consideration of resource allocation. Expert Syst. Appl. 38, 1980–1992 (2011)CrossRefGoogle Scholar
  29. Inuiguchi, M., Miyajima, T.: Rough set based rule induction from two decision tables. Eur. J. Oper. Res. 181, 1540–1553 (2007)MATHCrossRefGoogle Scholar
  30. Jaafar, A.F.B., Jais, J., Hamid, M.H.B.H.A., Rahman, Z.B.A., Benaouda, D.: Using rough set as a tool for knowledge discovery in DSS. In: Proceedings of the 4th International Conference on Multimedia and Information and Communication Technologies in Education, pp. 1011–1015, Seville, Spain (2006)Google Scholar
  31. 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
  32. Jensen, R., Shen, Q.: Semantics-preserving dimensionality reduction: rough and fuzzy-rough based approaches. IEEE Trans. Knowl. Data Eng. 16, 1457–1471 (2004)CrossRefGoogle Scholar
  33. Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: A rough set perspective on data and knowledge. In: Klösgen, W., Zytkow, J.M., Klosgen, W., Zyt, J. (eds.) The Handbook of Data Mining and Knowledge Discovery. Oxford University Press, New York (1999)Google Scholar
  34. Kondo, M.: On the structure of generalized rough sets. Inf. Sci. 176, 589–600 (2006)MathSciNetMATHCrossRefGoogle Scholar
  35. Leung, Y., Wu, W., Zhang, W.: Knowledge acquisition in incomplete information systems: a rough set approach. Eur. J. Oper. Res. 168, 164–180 (2006)MathSciNetMATHCrossRefGoogle Scholar
  36. Liao, S.-H., Chen, Y.-J., Chu, P.-H.: Rough-set-based association rules applied to brand trust evaluation model. Lect. Notes Comp. Sci. 6443, 634–641 (2010)CrossRefGoogle Scholar
  37. Lin, C.-S., Tzeng, G.-H., Chin, Y.-C.: Combined rough set theory and flow network graph to predict customer churn in credit card accounts. Expert Syst. Appl. 38, 8–15 (2011)CrossRefGoogle Scholar
  38. Liu, S., Chan, F.T.S., Chung, S.H.: A study of distribution center location based on the rough sets and interactive multi-objective fuzzy decision theory. Robot. Comput. Integrated Manuf. 27, 426–433 (2011)CrossRefGoogle Scholar
  39. Machowski, L.A., Marwala, T.: Using object oriented calculation process framework and neural networks for classification of image shapes. Int. J. Innov. Comput, Info. Control 1, 609–623 (2005)Google Scholar
  40. Marwala, T.: Computational Intelligence for Missing Data Imputation, Estimation and Management: Knowledge Optimization Techniques. IGI Global Publications, New York (2009)CrossRefGoogle Scholar
  41. Marwala, T., Crossingham, B.: Bayesian rough sets. ICIC Exp. Lett. 3, 115–120 (2009)Google Scholar
  42. Marwala, T., Crossingham, B.: Neuro-rough models for modelling HIV. In: Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp. 3089–3095, Singapore (2008)Google Scholar
  43. Nelwamondo, F.V.: Computational intelligence techniques for missing data imputation. Ph.D. thesis, University of the Witwatersrand, Johannesburg (2008)Google Scholar
  44. Ohrn, A.: Discernibility and rough sets in medicine: tools and applications. Unpublished Ph.D. thesis, Norwegian University of Science and Technology, Trondheim (1999)Google Scholar
  45. Ohrn, A., Rowland, T.: Rough sets: a knowledge discovery technique for multifactorial medical outcomes. Am. J. Phys. Med. Rehabil. 79, 100–108 (2000)CrossRefGoogle Scholar
  46. Pawlak, Z.: Rough Sets – Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)MATHGoogle Scholar
  47. Pawlak, Z., Skowron, A.: Rough sets and boolean reasoning. Inf. Sci. 177, 41–73 (2007)MathSciNetMATHCrossRefGoogle Scholar
  48. Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. Int. J. Man. Mach. Stud. 29, 81–95 (1988)MATHCrossRefGoogle Scholar
  49. Pawlak, Z., Munakata, T.: Rough control application of rough set theory to control. In: Proceedings of the 4th European Congress on Intelligent Techniques and Soft Computing, pp. 209–218, Aachen, Germany (1996)Google Scholar
  50. Quafafou, M.: α-RST: a generalization of rough set theory. Inf. Sci. 124, 301–316 (2000)MathSciNetMATHCrossRefGoogle Scholar
  51. Rowland, T., Ohno-Machado, L., Ohrn, A.: Comparison of multiple prediction models for ambulation following spinal cord injury. In Chute 31, 528–532 (1998)Google Scholar
  52. Salamó, M., López-Sánchez, M.: Rough set based approaches to feature selection for case-based reasoning classifiers. Pattern Recogn. Lett. 32, 280–292 (2011)CrossRefGoogle Scholar
  53. Shan, N., Ziarko, W.: Data-based acquisition and incremental modification of classification rules. Comput. Intell. 11, 357–370 (1995)CrossRefGoogle Scholar
  54. Slezak, D., Ziarko, W.: The investigation of the bayesian rough set model. Int. J. Approx Reason. 40, 81–91 (2005)MathSciNetMATHCrossRefGoogle Scholar
  55. Stefanowski, J.: On rough set based approaches to induction of decision rules. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1: Methodology and Applications. Physica-Verlag, Heidelberg (1998)Google Scholar
  56. Terlecki, P., Walczak, K.: On the relation between rough set reducts and jumping emerging patterns. Inf. Sci. 177, 74–83 (2007)MathSciNetMATHCrossRefGoogle Scholar
  57. Tettey, T., Nelwamondo, F.V., Marwala, T.: HIV Data analysis via rule extraction using rough sets. In: Proceedings of the 11th IEEE International Conference on Intelligent Engineering Systems, pp. 105–110, Budapest (2007)Google Scholar
  58. Wang, W., Yang, J., Jensen, R., Liu, X.: Rough set feature selection and rule induction for prediction of malignancy degree in brain glioma. Comput. Meth. Prog. Bio. 83, 147–156 (2006)CrossRefGoogle Scholar
  59. Wang, J., Guo, K., Wang, S.: Rough set and tabu search based feature selection for credit scoring. Procedia Comput. Sci. 1, 2433–2440 (2010)CrossRefGoogle Scholar
  60. Witlox, F., Tindemans, H.: The application of rough sets analysis in activity based modelling: opportunities and constraints. Expert Syst. Appl. 27, 585–592 (2004)CrossRefGoogle Scholar
  61. Wright, S., Marwala, T.: Artificial intelligence techniques for steam generator modelling. arXiv:0811.1711 (2006)
  62. Wu, W., Mi, J., Zhang, W.: Generalized fuzzy rough sets. Inf. Sci. 151, 263–282 (2003)MathSciNetMATHCrossRefGoogle Scholar
  63. Xie, F., Lin, Y., Ren, W.: Optimizing model for land use/land cover retrieval from remote sensing imagery based on variable precision rough sets. Ecol. Model. 222, 232–240 (2011)CrossRefGoogle Scholar
  64. Yan, W., Liu, W., Cheng, Z., Kan, J.: The prediction of soil moisture based on rough set-neural network model. In: Proceedings of the 29th Chinese Control Conference, pp. 2413–2415, Beijing (2010)Google Scholar
  65. Yang, Y., John, R.: Roughness bound in set-oriented rough set operations. In: Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 1461–1468, Vancouver (2006)Google Scholar
  66. Yao, J.T., Yao, Y.Y.: Induction of classification rules by granular computing. In: Proceedings of the Third International Conference on Rough Sets and Current Trends in Comput, pp. 331–338, Malvern (2002)Google Scholar
  67. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)MathSciNetMATHCrossRefGoogle Scholar
  68. Zhang, L., Shao, C.: Designing fuzzy inference system based on improved gradient descent method. J. Syst. Eng. Electron. 17, 853–857 (2006)MATHCrossRefGoogle Scholar
  69. Zhang, Y., Zhu, J., Zhang, Z-Y.: The research of reagent adding control in anionic reverse flotation process based on rough set theory. In: Proceedings of the 29th Chinese Control Conference, pp. 3487–3491, Beijing (2010)Google Scholar
  70. Zhao, Y., Yao, Y., Luo, F.: Data analysis based on discernibility and indiscernibility. Inf. Sci. 177, 4959–4976 (2007)MATHCrossRefGoogle Scholar
  71. Ziarko, W.: Rough sets as a methodology for data mining. In: Polkowski, L. (ed.) Rough Sets in Knowledge Discovery 1: Methodology and Applications. Physica-Verlag, Heidelberg (1998)Google Scholar
  72. Zou, Z., Tseng, T.-L., Sohn, H., Song, G., Gutierrez, R.: A rough set based approach to distributor selection in supply chain management. Expert Syst. Appl. 38, 106–115 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.University of JohannesburgJohannesburgSouth Africa

Personalised recommendations