Advertisement

Fuzzy Rules Tuning for Direct Inference

  • Alexander P. Rotshtein
  • Hanna B. Rakytyanska
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 275)

Abstract

The identification of an object consists of the construction of its mathematical model, i.e., an operator of connection between input and output variables from experimental data. Modern identification theory [1 – 3], based on modeling dynamical objects by equations (differential, difference, etc.), is poorly suited for the use of information about an object in the form of expert IF-THEN statements. Such statements are concentrated expertise and play an important role in the process of human solution of various cybernetic problems: control of technological processes, pattern recognition, diagnostics, forecast, etc. The formal apparatus for processing expert information in a natural language is fuzzy set theory [4, 5]. According to this theory, a model of an object is given in the form of a fuzzy knowledge base, which is a set of IF-THEN rules that connect linguistic estimates for input and output object variables. The adequacy of the model is determined by the quality of the membership functions, by means of which linguistic estimates are transformed into a quantitative form. Since membership functions are determined by expert methods [5], the adequacy of the fuzzy model depends on the expert qualification.

Keywords

Membership Function Fuzzy Rule Fuzzy Model Direct Inference Rule Weight 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Eickhoff, P.: Principles of Identification of Control Systems, p. 321. Mir, Moscow (1975) (in Russian)Google Scholar
  2. 2.
    Tsypkin, Y.: Information Theory of Identification. Nauka, Moscow (1984)zbMATHGoogle Scholar
  3. 3.
    Shteinberg, S.E.: Identification in Control Systems, p. 81. Energoatomizdat, Moscow (1987) (in Russian) Google Scholar
  4. 4.
    Zadeh, L.: Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Transactions on Systems, Man, and Cybernetics SMC-3, 28–44 (1973)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zimmermann, H.-J.: Fuzzy Set Theory and Its Application. Kluwer, Dordrecht (1991)Google Scholar
  6. 6.
    Rotshtein, A.: Design and Tuning of Fuzzy Rule-Based Systems for Medical Diagnostics. In: Teodorescu, N.-H., Kandel, A. (eds.) Fuzzy and Neuro-Fuzzy Systems in Medicine, pp. 243–289. CRC Press, New York (1998)Google Scholar
  7. 7.
    Rotshtein, A.: Intellectual Technologies of Identification: Fuzzy Sets, Genetic Algorithms, Neural Nets, p. 320. UNIVERSUM, Vinnitsa (1999) (in Russian) , http://matlab.exponenta.ru/fuzzylogic/book5/index.php Google Scholar
  8. 8.
    Rotshtein, A., Katel’nikov, D.: Identification of Non-linear Objects by Fuzzy Knowledge Bases. Cybernetics and Systems Analysis 34(5), 676–683 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Rotshtein, A., Loiko, E., Katel’nikov, D.: Prediction of the Number of Diseases on the basis of Expert-linguistic Information. Cybernetics and Systems Analysis 35(2), 335–342 (1999)zbMATHCrossRefGoogle Scholar
  10. 10.
    Rotshtein, A., Mityushkin, Y.: Neurolinguistic Identification of Nonlinear Dependencies. Cybernetics and Systems Analysis 36(2), 179–187 (2000)zbMATHCrossRefGoogle Scholar
  11. 11.
    Rotshtein, A., Mityushkin, Y.: Extraction of Fuzzy Knowledge Bases from Experimental Data by Genetic Algorithms. Cybernetics and Systems Analysis 37(4), 501–508 (2001)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Rotshtein, A.P., Shtovba, S.D.: Managing a Dynamic System by means of a Fuzzy Knowledge Base. Automatic Control and Computer Sciences 35(2), 16–22 (2001)Google Scholar
  13. 13.
    Rotshtein, A.P., Posner, M., Rakytyanska, H.: Adaptive System for On-line Prediction of Diseases Evolution. In: Mastorakis, D. (ed.) Advances in Neural World. Lectures and Books Series, pp. 178–183. WSEAS, Switzerland (2002)Google Scholar
  14. 14.
    Rotshtein, A.P., Posner, M., Rakytyanska, H.B.: Football Predictions based on a Fuzzy Model with Genetic and Neural Tuning. Cybernetics and Systems Analysis 41(4), 619–630 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Rotshtein, A.P., Rakytyanska, H.B.: Fuzzy Forecast Model with Genetic-Neural Tuning. Journal of Computer and Systems Sciences International 44(1), 102–111 (2005)zbMATHGoogle Scholar
  16. 16.
    Terano, T., Asai, K., Sugeno, M. (eds.): Applied Fuzzy Systems. Omsya, Tokyo (1989); Moscow, Mir (1993) (in Russian)zbMATHGoogle Scholar
  17. 17.
    Rotshtein, A.: Modification of Saaty Method for the Construction of Fuzzy Set Membership Functions. In: FUZZY 1997 – Int. Conf. Fuzzy Logic and Its Applications in Zichron, Yaakov, Israel, pp. 125–130 (1997)Google Scholar
  18. 18.
    Gen, M., Cheng, R.: Genetic Algorithms and Engineering Design, p. 352. John Wiley & Sons, New York (1997)Google Scholar
  19. 19.
    Ivachnenko, A.G., Lapa, V.G.: Forecasting of Random Processes, p. 416. Naukova dumka, Kiev (1971) (in Russian)Google Scholar
  20. 20.
    Markidakis, S., Wheelwright, S.C., Hindman, R.J.: Forecasting: Methods and Applications, 3rd edn., p. 386. John Wiley & Sons, USA (1998)Google Scholar
  21. 21.
    Mayoraz, F., Cornu, T., Vulliet, L.: Prediction of slope movements using neural networks. Fuzzy Systems Artif. Intel. 4(1), 9–17 (1995)Google Scholar
  22. 22.
    Nie, J.: Nonlinear Time Series Forecasting: A Fuzzy Neural Approach. Neuro Computing 16(1), 63–76 (1997)Google Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander P. Rotshtein
    • 1
  • Hanna B. Rakytyanska
    • 2
  1. 1.Department of Industrial Engineering and ManagementJerusalem College of Technology - Lev InstituteJerusalemIsrael
  2. 2.Department of Software DesignVinnytsia National Technical UniversityVinnitsaUkraine

Personalised recommendations