Decisions Tree Learning Method Based on Three-Way Decisions

  • Yangyang Liu
  • Jiucheng Xu
  • Lin Sun
  • Lina Du
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9437)


Aiming at the problems that traditional data mining methods ignore inconsistent data, and general decision tree learning algorithms lack of theoretical support for the classification of inconsistent nodes. The three-way decision is introduced to decision tree learning algorithms,and the decision tree learning method based on three-way decisions is proposed. Firstly, the proportion of positive objects in node is used to compute the conditional probability of the three-way decision of node. Secondly, the nodes in decision tree arepartitioned to generate the three-way decision tree. The merger and pruning rules of the three-way decision tree are derived to convert the three-way decision tree into two-way decision tree by considering the information around nodes. Finally, an exampleisimplemented. The results show that the proposed method reserves inconsistent information, partitions inconsistent nodes by minimizing the overall risk, not only generates decision tree with cost-sensitivity, but also makes the partition of inconsistent nodes more explicable. Besides, the proposed method reduces the overfitting to some extent and the computation problem of conditional probability of three-way decisions is resolved.


Three-way decisions Decision tree Conditional probability Boundary nodes Minimizing the overall risk Merger and pruning 



The authors wish to thank the anonymous reviewers and Editor-in-Chief for their valuable comments and hard work. This work was supported by the National Natural Science Foundation of China (Nos. 61370169, 61402153,60873104), the Key Project of Science and Technology Department of Henan Province (Nos. 142102210056, 112102210194), the Science and Technology Research Key Project of Educational Department of Henan Province (Nos.12A520027, 13A520529), the Key Project of Science and Technology of Xinxiang Government (No. ZG13004), the Education Fund for Youth Key Teachers of Henan Normal University, and the 2014 Henan Normal University Youth Science Fund(No. 2014QK28).


  1. 1.
    Qian, W.B., Yang, B.R., Xu, Z.Y., Xie, Y.H.: Rule extraction algorithm based on discernibility matrix in inconsistent decision table. Comput. Sci. 40(6), 215–218 (2013)Google Scholar
  2. 2.
    Meng, Z.Q., Zhou, S.Q.: Research method of generalized decision rule acquisition based on GrC in inconsistent decision systems. Comput. Sci. 39(1), 198–202 (2012)MathSciNetGoogle Scholar
  3. 3.
    Diogo, R., Ferreira, E.V.: Using logical decision trees to discover the cause of process delays from event logs. Comput. Ind. 70, 194–207 (2015)CrossRefGoogle Scholar
  4. 4.
    Hong, K.S., Melanie, P.O., Ye, C.K.: Sparse alternating decision tree. Pattern Recogn. Lett. 60, 57–64 (2015)Google Scholar
  5. 5.
    Mistikoglu, G., Gerek, I.H., Erdis, E., Mumtaz Usmen, P.E., Cakan, H., Kazan, E.E.: Decision tree analysis of construction fall accidents involving roofers. Expert Syst. Appl. 42(4), 2256–2263 (2015)CrossRefGoogle Scholar
  6. 6.
    Chen, J.K., Wang, X.Z., Gao, X.H.: Improved ordinal decisions trees algorithms based on rank entropy. Pattern Recogn. Artif. Intell. 27(2), 134–140 (2014)Google Scholar
  7. 7.
    Ruan, X.H., Huang, X.M., Yuan, D.R., Duan, Q.L.: Classification algorithm based on heterogeneous cost-sensitive decision tree. Comput. Sci. 40(11A), 140–142 (2013)Google Scholar
  8. 8.
    Jia, X.Y., Shang, L., Zhou, X.Z., Liang, J.Y., Miao, D.Q., Wang, G.Y., Li, T.R., Zhang, Y.P.: The Theory and Application of Three-way Decision. Nanjing University Press, Nanjing (2012)Google Scholar
  9. 9.
    Liu, D., Li, T., Liang, D.: A new discriminant analysis approach under decision-theoretic rough sets. In: Yao, J.T., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 476–485. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  10. 10.
    Yao, Y., Zhou, B.: Naive bayesian rough sets. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.) RSKT 2010. LNCS, vol. 6401, pp. 719–726. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  11. 11.
    Jia, X.Y., Tang, Z.M., Liao, W.H., Shang, L.: On an optimization representation of decision-theoretic rough set model. Int. J. Approximate Reasoning 55(1), 156–166 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Li, H.X., Zhou, X.Z., Zhao, J.B.: Non-nonotonic attribute reduction indecision-theoretic rough sets. Fundamenta Informaticae 126(4), 415–432 (2013)MathSciNetGoogle Scholar
  13. 13.
    Liu, D., Li, T.R., Liang, D.C.: Incorporating logistic regression to decisiontheoretic rough sets for classifications. Int. J. Approximate Reasoning 55(1), 197–210 (2014)zbMATHCrossRefGoogle Scholar
  14. 14.
    Li, H.: Statistical Learning Method. Tsinghua University Press, Beijing (2012) Google Scholar
  15. 15.
    Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180(3), 341–353 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Liu, D., Li, T.R., Liang, D.C.: Incorporating logistic regression to decision-theoretic rough sets for classifications. Int. J. Approximate Reasoning 55, 197–210 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Liu, D., Yao, Y.Y., Li, T.R.: Three-way decision-theoretic rough sets. Comput. Sci. 38(1), 246–250 (2011)Google Scholar
  18. 18.
    Yao, Y.: Three-way decision: an interpretation of rules in rough set theory. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds.) RSKT 2009. LNCS, vol. 5589, pp. 642–649. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  19. 19.
    Liu, D., Li, T.R., Liang, D.C.: Incorporating logistic regression to decision-theoretic rough sets for classifications. Int. J. Approximate Reasoning 55(1), 197–210 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Liu, D., Li, T.R., Li, H.X.: Rough set theory: a three-way decisions perspective. J. Nanjing Univ. (Natural Sciences) 49(5), 574–581 (2013)MathSciNetzbMATHGoogle Scholar

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Authors and Affiliations

  • Yangyang Liu
    • 1
  • Jiucheng Xu
    • 1
    • 2
    • 3
  • Lin Sun
    • 1
    • 2
    • 3
  • Lina Du
    • 1
  1. 1.College of Computer and Information EngineeringHenan Normal UniversityXinxiangChina
  2. 2.Engineering Technology Research Center for Computing Intelligence and Data MiningXinxiangChina
  3. 3.Engineering Laboratory of Intellectual Business and Internet of Things TechnologiesXinxiangChina

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