Sequential Classification Via Fuzzy Relations

  • Marek Kurzynski
  • Andrzej Zolnierek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4029)


In this paper there are developed and evaluated methods for performing sequential classification (SC) using fuzzy relations defined on product of class set and fuzzified feature space. First on the base of learning set, fuzzy relation in the proposed method is determined as a solution of appropriate optimization problem. Next, this relation in the form of matrix of membership degrees is used at successive instants of sequential decision process. Three various algorithms of SC which differ both in the sets of input data and procedure are described. Proposed algorithms were practically applied to the computer-aided recognition of patient’s acid-base equilibrium states where as an optimization procedure the real-coded genetic algorithm (RGA) was used.


Feature Space Membership Degree Fuzzy Relation Fuzzy Relation Equation Sequential Decision Process 
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.


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  1. 1.
    Toussaint, G.: The Use of Context in Pattern Recognition. Pattern Recognition 10, 189–204 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Kurzynski, M.: Benchmark of Approaches to Sequential Diagnosis. In: Lisboa, P., Ifeachor, J., Szczepaniak, P. (eds.) Perspectives in Neural Computing, pp. 129–140. Springer, Heidelberg (1998)Google Scholar
  3. 3.
    Kurzynski, M.: Multistage Diagnosis of Myocardial Infraction Using a Fuzzy Relation. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 1014–1019. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Zolnierek, A.: The Empirical Study of the Naive Bayes Classifier in the Case of Markov Chain Recognition Task. In: Kurzynski, M., Wozniak, M. (eds.) Computer Recognition Systems CORES 2005, pp. 329–336. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Devroye, L., Gyorfi, P., Lugossi, G.: A Probabilistic Theory of Pattern Recognition. Springer, Heidelberg (1996)zbMATHGoogle Scholar
  6. 6.
    Duda, R., Hart, P., Stork, D.: Pattern Classification. John Wiley and Sons, New York (2001)zbMATHGoogle Scholar
  7. 7.
    Czogala, E., Leski, J.: Fuzzy and Neuro-Fuzzy Intelligent Systems. Springer, Heidelberg (2000)zbMATHGoogle Scholar
  8. 8.
    Michalewicz, Z.: Genetic Algorithms + Data Structure = Evolution Programs. Springer, New York (1996)Google Scholar
  9. 9.
    Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning. Adison-Wesley, New York (1989)zbMATHGoogle Scholar
  10. 10.
    Herrera, F., Lozano, M.: Gradual Distributed Real-Coded Genetic Algorithm. IEEE Trans. on Evolutionary Computing 4, 43–63 (2000)CrossRefGoogle Scholar
  11. 11.
    Pedrycz, W.: Fuzzy Sets in Pattern Recognition: Methodology and Methods. Pattern Recognition 23, 121–146 (1990)CrossRefGoogle Scholar
  12. 12.
    Pedrycz, W.: Genetic Algorithms for Learning in Fuzzy Relation Structures. Fuzzy Sets Syst. 69, 37–45 (1995)CrossRefGoogle Scholar
  13. 13.
    Ray, K., Dinda, T.: Pattern Classification Using Fuzzy Relational Calculus. IEEE Trans. SMC 33, 1–16 (2003)Google Scholar
  14. 14.
    Dinola, A., Pedrycz, W., Sessa, S.: Fuzzy Relation Equations Theory as a Basis of Fuzzy Modelling: An Overview. Fuzzy Sets Syst. 40, 415–429 (1991)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Ovchinnikov, S., Riera, T.: On Fuzzy Classifications. Fuzzy Sets Syst. 49, 119–132 (1992)CrossRefGoogle Scholar
  16. 16.
    Gottwald, S.: Approximately Solving Fuzzy Relation Equations: Some Mathematical Results and Some Heuristic Proposals. Fuzzy Sets Syst. 66, 175–193 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Setnes, M., Babuska, R.: Fuzzy Relational Classifier Trained by Fuzzy Clustering. IEEE Trans. on SMC 29, 619–625 (1999)Google Scholar
  18. 18.
    Acharya, U., et al.: Classification of Heart Rate Data Using Artificial Neural Network and Fuzzy Equivalence Relation. Pattern Recognition 36, 61–68 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marek Kurzynski
    • 1
  • Andrzej Zolnierek
    • 1
  1. 1.Faculty of Electronics, Chair of Systems and Computer NetworksWroclaw University of TechnologyWroclawPoland

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