On the Number of Rules and Conditions in Mining Data with Attribute-Concept Values and “Do Not Care” Conditions

  • Patrick G. Clark
  • Jerzy W. Grzymala-BusseEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9124)


In this paper we discuss two interpretations of missing attribute values: attribute-concept values and “do not care” conditions. Experiments were conducted on eight kinds of data sets, using three types of probabilistic approximations: singleton, subset and concept. Rules were induced by the MLEM2 rule induction system. Our main objective was to test which interpretation of missing attribute values provides simpler rule sets in terms of the number of rules and the total number of conditions. Our main result is that experimental evidence exists showing rule sets induced from data sets with attribute-concept values are simpler than the rule sets induced from “do not care” conditions.


Probabilistic Approximation Decision Table Breast Cancer Data Indiscernibility Relation Rule Induction Algorithm 
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. 1.
    Clark, P.G., Grzymala-Busse, J.W.: Experiments on probabilistic approximations. In: Proceedings of the 2011 IEEE International Conference on Granular Computing, pp. 144–149 (2011)Google Scholar
  2. 2.
    Clark, P.G., Grzymala-Busse, J.W.: Complexity of rule sets induced from incomplete data sets with attribute-concept values and and “do not care” conditions. In: Proceedings of the Third International Conference on Data Management Technologies and Applications, pp. 56–63 (2014)Google Scholar
  3. 3.
    Clark, P.G., Grzymala-Busse, J.W.: Mining incomplete data with attribute-concept values and “do not care” conditions. In: Polycarpou, M., de Carvalho, A.C.P.L.F., Pan, J.-S., Woźniak, M., Quintian, H., Corchado, E. (eds.) HAIS 2014. LNCS, vol. 8480, pp. 156–167. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  4. 4.
    Grzymala-Busse, J.W.: On the unknown attribute values in learning from examples. In: Raś, Zbigniew W., Zemankova, M. (eds.) ISMIS 1991. LNCS, vol. 542, pp. 368–377. Springer, Heidelberg (1991) CrossRefGoogle Scholar
  5. 5.
    Grzymala-Busse, J.W.: LERS—a system for learning from examples based on rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Set Theory, pp. 3–18. Kluwer Academic Publishers, Dordrecht (1992)CrossRefGoogle Scholar
  6. 6.
    Grzymala-Busse, J.W.: A new version of the rule induction system LERS. Fundamenta Informaticae 31, 27–39 (1997)zbMATHGoogle Scholar
  7. 7.
    Grzymala-Busse, J.W.: MLEM2: a new algorithm for rule induction from imperfect data. In: Proceedings of the 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 243–250 (2002)Google Scholar
  8. 8.
    Grzymala-Busse, J.W.: Rough set strategies to data with missing attribute values. In: Notes of the Workshop on Foundations and New Directions of Data Mining, in conjunction with the Third International Conference on Data Mining, pp. 56–63 (2003)Google Scholar
  9. 9.
    Grzymała-Busse, J.W.: Characteristic relations for incomplete data: a generalization of the indiscernibility relation. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 244–253. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  10. 10.
    Grzymala-Busse, J.W.: Data with missing attribute values: generalization of indiscernibility relation and rule induction. Trans. Rough Sets 1, 78–95 (2004)Google Scholar
  11. 11.
    Grzymala-Busse, J.W.: Three approaches to missing attribute values—a rough set perspective. In: Proceedings of the Workshop on Foundation of Data Mining, in conjunction with the Fourth IEEE International Conference on Data Mining, pp. 55–62 (2004)Google Scholar
  12. 12.
    Grzymała-Busse, J.W.: Generalized parameterized approximations. In: Yao, J.T., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 136–145. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  13. 13.
    Kryszkiewicz, M.: Rough set approach to incomplete information systems. In: Proceedings of the Second Annual Joint Conference on Information Sciences, pp. 194–197 (1995)Google Scholar
  14. 14.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Pawlak, Z., Skowron, A.: Rough sets: some extensions. Inf. Sci. 177, 28–40 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. Int. J. Man Mach. Stud. 29, 81–95 (1988)zbMATHCrossRefGoogle Scholar
  17. 17.
    Ślȩzak, D., Ziarko, W.: The investigation of the bayesian rough set model. Int. J. Approximate Reasoning 40, 81–91 (2005)CrossRefGoogle Scholar
  18. 18.
    Stefanowski, J., Tsoukias, A.: On the extension of rough sets under incomplete information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 73–82. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  19. 19.
    Yao, Y.Y.: Probabilistic rough set approximations. Int. J. Approximate Reasoning 49, 255–271 (2008)zbMATHCrossRefGoogle Scholar
  20. 20.
    Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximate concepts. Int. J. Man Mach. Stud. 37, 793–809 (1992)CrossRefGoogle Scholar
  21. 21.
    Ziarko, W.: Probabilistic approach to rough sets. Int. J. Approximate Reasoning 49, 272–284 (2008)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of KansasLawrenceUSA
  2. 2.Department of Expert Systems and Artificial IntelligenceUniversity of Information Technology and ManagementRzeszowPoland

Personalised recommendations