TSK Inference with Sparse Rule Bases

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 513)


The Mamdani and TSK fuzzy models are fuzzy inference engines which have been most widely applied in real-world problems. Compared to the Mamdani approach, the TSK approach is more convenient when the crisp outputs are required. Common to both approaches, when a given observation does not overlap with any rule antecedent in the rule base (which usually termed as a sparse rule base), no rule can be fired, and thus no result can be generated. Fuzzy rule interpolation was proposed to address such issue. Although a number of important fuzzy rule interpolation approaches have been proposed in the literature, all of them were developed for Mamdani inference approach, which leads to the fuzzy outputs. This paper extends the traditional TSK fuzzy inference approach to allow inferences on sparse TSK fuzzy rule bases with crisp outputs directly generated. This extension firstly calculates the similarity degrees between a given observation and every individual rule in the rule base, such that the similarity degrees between the observation and all rule antecedents are greater than 0 even when they do not overlap. Then the TSK fuzzy model is extended using the generated matching degrees to derive crisp inference results. The experimentation shows the promising of the approach in enhancing the TSK inference engine when the knowledge represented in the rule base is not complete.


  1. 1.
    Mamdani, E.H.: Application of fuzzy logic to approximate reasoning using linguistic synthesis. IEEE Trans. Comput. C-26(12), 1182–1191 (1977)Google Scholar
  2. 2.
    Takagi, T., Sugeno. M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. SMC-15(1), 116–132 (1985)Google Scholar
  3. 3.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning - i. Inf. Sci. 8(3), 199–249 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lee, C.C.: Fuzzy logic in control systems: fuzzy logic controller. ii. IEEE Trans. Syst. Man Cybern. 20(2), 419–435 (1990)Google Scholar
  5. 5.
    Kóczy, L., Hirota, K.: Approximate reasoning by linear rule interpolation and general approximation. Int. J. Approx. Reason. 9(3), 197–225 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Huang, Z., Shen, Q.: Fuzzy interpolative reasoning via scale and move transformations. IEEE Trans. Fuzzy Syst. 14(2), 340–359 (2006)CrossRefGoogle Scholar
  7. 7.
    Huang, Z., Shen, Q.: Fuzzy interpolation and extrapolation: a practical approach. IEEE Trans. Fuzzy Syst. 16(1), 13–28 (2008)CrossRefGoogle Scholar
  8. 8.
    Yang, L., Shen, Q.: Adaptive fuzzy interpolation and extrapolation with multiple-antecedent rules. In: 2010 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1–8 (2010)Google Scholar
  9. 9.
    Yang, L., Shen, Q.: Adaptive fuzzy interpolation. IEEE Trans. Fuzzy Syst. 19(6), 1107–1126 (2011)CrossRefGoogle Scholar
  10. 10.
    Yang, L., Shen, Q.: Closed form fuzzy interpolation. Fuzzy Sets Syst. 225, 1–22 (2013)Google Scholar
  11. 11.
    Li, J., Yang, L., Shum, P.H., Sexton, G., Tan, Y.: Intelligent home heating controller using fuzzy rule interpolation. In: UK Workshop on Computational Intelligence (2015)Google Scholar
  12. 12.
    Molnarka, G.I., Kovacs, S., Kóczy, L.T.: Fuzzy rule interpolation based fuzzy signature structure in building condition evaluation. In: 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 2214–2221 (2014)Google Scholar
  13. 13.
    Chen, S.M.: New methods for subjective mental workload assessment and fuzzy risk analysis. Cybern. Syst. 27(5), 449–472 (1996)CrossRefzbMATHGoogle Scholar
  14. 14.
    Sridevi, B., Nadarajan, R.: Fuzzy similarity measure for generalized fuzzy numbers. Int. J. Open Problems Compt. Math 2(2), 242–253 (2009)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Chen, S.J., Chen, S.M.: Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Trans. Fuzzy Syst. 11(1), 45–56 (2003)CrossRefGoogle Scholar
  16. 16.
    Niyigena, L., Luukka, P., Collan, M.: Supplier evaluation with fuzzy similarity based fuzzy topsis with new fuzzy similarity measure. In: 2012 IEEE 13th International Symposium on Computational Intelligence and Informatics (CINTI), pp. 237–244 (2012)Google Scholar
  17. 17.
    Chen, S.H., Hsieh, C.H.: Ranking generalized fuzzy number with graded mean integration representation. In: Proceedings of the Eighth International Conference of Fuzzy Sets and Systems Association World Congress, vol. 2, pp. 551–555 (1999)Google Scholar
  18. 18.
    Angelov, P.: Autonomous learning systems: from data streams to knowledge in real-time, J Wiley and Sons, (2012)Google Scholar
  19. 19.
    Bellaaj, H., Ketata, R., Chtourou, M.: A new method for fuzzy rule base reduction. J. Intell. Fuzzy Syst. 25(3), 605–613 (2013)Google Scholar
  20. 20.
  21. 21.
    Rezaee, B., Zarandi, M.H.F.: Data-driven fuzzy modeling for takagi-sugeno-kang fuzzy system. Inf. Sci. 180(2), 241–255 (2010)Google Scholar
  22. 22.
    Li, J., Shum, H.P.H., Fu, X., Sexton, G., Yang, L.: Experience-based rule base generation and adaptation for fuzzy interpolationn. In: IEEE World Congress on Computation Intelligence Internation Conference (2016)Google Scholar
  23. 23.
    Tan, Y., Li, J., Wonders, M., Chao, F., Shum, H.P.H., Yang, L.: Towards sparse rule base generation for fuzzy rule interpolation. In: IEEE World Congress on Computation Intelligence Internation Conference (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculty of Engineering and EnvironmentNorthumbria UniversityNewcastle upon TyneUK
  2. 2.Information Science and Technology CollegeDalian Maritime UniversityDalianChina

Personalised recommendations