Skip to main content

Part of the book series: Topics in Intelligent Engineering and Informatics ((TIEI,volume 8))

  • 1026 Accesses

Abstract

The number of the Fuzzy Rule Interpolation (FRI) applications in engineering tasks is still insignificant compared to the classical fuzzy reasoning methods. The main goal of this paper is to emphasize the benefits of the direct (embedded) applicability of fuzzy rule interpolation and the related sparse rule-based knowledge representation through demonstrative examples in rather different areas. As a prerequisite of sparse rule-base application in fuzzy system the FRI methods have the benefit of providing reasonable (interpolated) conclusions even if none of the existing rules matches the current observation. In spite of the classical fuzzy reasoning methods this feature enables FRI systems to have knowledge representation similarly constructed as expert systems, built upon the definition of cardinal rules only. On the other hand, thanks to the fuzzy concept, the fuzzy set symbol representation and the fuzzy reasoning, the discretely defined rules can act on continuous universes and continuous states. After a short discussion of FRI methods the paper will briefly introduce four FRI embedded application example of rule-based knowledge representation acting on continuous domain problems selected from the last 15 years work of our research group.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. on SMC (3), 28–44 (1973)

    Google Scholar 

  2. Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. of Man Machine Studies (7), 1–13 (1975)

    Google Scholar 

  3. Larsen, P.M.: Industrial application of fuzzy logic control. Int. J. of Man Machine Studies 12(4), 3–10 (1980)

    Article  Google Scholar 

  4. Sugeno, M.: An introductory survey of fuzzy control. Information Science (36), 59–83 (1985)

    Google Scholar 

  5. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. on SMC (15), 116–132 (1985)

    Google Scholar 

  6. Kóczy, L.T., Hirota, K.: Rule interpolation by α-level sets in fuzzy approximate reasoning. J. BUSEFAL, Automne, URA-CNRS 46, 115–123 (1991)

    Google Scholar 

  7. Kóczy, L.T., Kovács, S.: On the preservation of the convexity and piecewise linearity in linear fuzzy rule interpolation. Tokyo Inst. Technol., Yokohama, Japan, Tech. Rep. TR 93-94/402, LIFE Chair Fuzzy Theory (1993)

    Google Scholar 

  8. Kóczy, L.T., Kovács, S.: Shape of the Fuzzy Conclusion Generated by Linear Inter-polation in Trapezoidal Fuzzy Rule Bases. In: Proceedings of the 2nd European Congress on Intelligent Techniques and Soft Computing, Aachen, pp. 1666–1670 (1994)

    Google Scholar 

  9. Vass, G., Kalmár, L., Kóczy, L.T.: Extension of the fuzzy rule interpolation method. In: Proc. Int. Conf. Fuzzy Sets Theory Applications (FSTA 1992), Liptovsky M., Czechoslovakia, pp. 1–6 (1992)

    Google Scholar 

  10. Tikk, D., Joó, I., Kóczy, L.T., Várlaki, P., Moser, B., Gedeon, T.D.: Stability of interpolative fuzzy KH-controllers. Fuzzy Sets and Systems 125(1), 105–119 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Tikk, D.: Notes on the approximation rate of fuzzy KH interpolator. Fuzzy Sets and Systems 138(2), 441–453 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Tikk, D., Baranyi, P.: Comprehensive analysis of a new fuzzy rule interpolation method. IEEE Trans. Fuzzy Syst. 8(3), 281–296 (2000)

    Article  Google Scholar 

  13. Yam, Y., Kóczy, L.T.: Representing membership functions as points in high dimensional spaces for fuzzy interpolation and extrapolation. Dept. Mech. Automat. Eng., Chinese Univ. Hong Kong, Tech. Rep.CUHK-MAE-97-03 (1997)

    Google Scholar 

  14. Tikk, D., Baranyi, P., Gedeon, T.D., Muresan, L.: Generalization of a rule interpolation method resulting always in acceptable conclusion. Tatra Mountains Math. Publ. 21, 73–91 (2001)

    MATH  MathSciNet  Google Scholar 

  15. Kóczy, L.T., Hirota, K., Gedeon, T.D.: Fuzzy rule interpolation by the conservation of relative fuzziness. Technical Report TR 97/2. Hirota Lab, Dept. of Comp. Int. and Sys. Sci., Tokyo Inst. of Techn., Yokohama (1997)

    Google Scholar 

  16. Wong, K.W., Gedeon, T.D., Tikk, D.: An improved multidimensional α-cut based fuzzy interpolation technique. In: Proc. Int. Conf Artificial Intelligence in Science and Technology (AISAT 2000), Hobart, Australia, pp. 29–32 (2000)

    Google Scholar 

  17. Wong, K.W., Tikk, D., Gedeon, T.D., Kóczy, L.T.: Fuzzy Rule Interpolation for Multidimensional Input Spaces With Applications. IEEE Transactions on Fuzzy Systems 13(6), 809–819 (2005)

    Article  Google Scholar 

  18. Bouchon-Meunier, B., Delechamp, J., Marsala, C., Mellouli, N., Rifqi, M., Zerrouki, L.: Analogy and fuzzy interpolation in case of sparse rules. In: Proceedings of the EUROFUSE-SIC Joint Conference, pp. 132–136 (1999)

    Google Scholar 

  19. Bouchon-Meunier, B., Marsala, C., Rifqi, M.: Interpolative reasoning based on graduality. In: Proceedings of FUZZ-IEEE 2000, International Conference, San Antonio, pp. 483–487 (2000)

    Google Scholar 

  20. Baranyi, P., Kóczy, L.T., Gedeon, T.D.: A Generalized Concept for Fuzzy Rule In-terpolation. IEEE Trans. on Fuzzy Systems 12(6), 820–837 (2004)

    Article  Google Scholar 

  21. Johanyák, Z.C., Kovács, S.: Fuzzy rule interpolation based on polar cuts. In: Reusch, B. (ed.) Computational Intelligence, Theory and Applications, pp. 499–511. Springer (2006)

    Google Scholar 

  22. Johanyák, Z.C.: Fuzzy Rule Interpolation based on Subsethood Values. In: Proceedings of 2010 IEEE Interenational Conference on Systems Man, and Cybernetics (SMC 2010), October 10-13, pp. 2387–2393 (2010) ISBN 978-1-424-6587-3

    Google Scholar 

  23. Huang, Z., Shen, Q.: Fuzzy interpolative reasoning via scale and move transformations. IEEE Trans. Fuzzy Syst. 14(2), 340–359 (2006)

    Article  Google Scholar 

  24. Kovács, S.: New Aspects of Interpolative Reasoning. In: Proceedings of the 6th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Granada, Spain, pp. 477–482 (1996)

    Google Scholar 

  25. Kovács, S., Kóczy, L.T.: Approximate Fuzzy Reasoning Based on Interpolation in the Vague Environment of the Fuzzy Rule base as a Practical Alternative of the Classical CRI. In: Proceedings of the 7th International Fuzzy Systems Association World Congress, Prague, Czech Republic, pp. 144–149 (1997)

    Google Scholar 

  26. Kovács, S., Kóczy, L.T.: The use of the concept of vague environment in approximate fuzzy reasoning. In: Fuzzy Set Theory and Applications, vol. 12, pp. 169–181. Tatra Mountains Mathematical Publications, Mathematical Institute Slovak Academy of Sciences, Bratislava, Slovak Republic (1997)

    Google Scholar 

  27. Klawonn, F.: Fuzzy Sets and Vague Environments. Fuzzy Sets and Systems 66, 207–221 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  28. Shepard, D.: A two dimensional interpolation function for irregularly spaced data. In: Proc. 23rd ACM Internat. Conf., pp. 517–524 (1968)

    Google Scholar 

  29. FRI Toolbox available at: http://fri.gamf.hu

  30. FRI applications are available at: http://www.iit.uni-miskolc.hu/~szkovacs

  31. Kovács, S., Kóczy, L.T.: Application of the Approximate Fuzzy Reasoning Based on Interpolation in the Vague Environment of the Fuzzy Rulebase in the Fuzzy Logic Controlled Path Tracking Strategy of Differential Steered AGVs. In: Reusch, B. (ed.) Fuzzy Days 1997. LNCS, vol. 1226, pp. 456–467. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  32. Kovács, S., Kóczy, L.T.: Path Tracking and Collision Avoidance Strategy of an AGV Implemented on Interpolation-based Fuzzy Logic Controller. In: Proceedings of the INES 1998 IEEE International Conference on Intelligent Engineering Systems, Vienna, Austria, pp. 67–72 (1998)

    Google Scholar 

  33. Kovács, S.: Fuzzy Behaviour-based Control Techniques in Adaptive System Applications. In: Proceedings of the IEEE International Conference on Computational Cybernetics, ICCC 2003, Siófok, Hungary, August 29-31, p. 6 (2003)

    Google Scholar 

  34. Kovács, S.: Fuzzy Rule Interpolation in Practice. In: Proceedings of the Joint 3rd International Conference on Soft Computing and Intelligent Systems and 7th International Symposium on advanced Intelligent Systems (SCIS & ISIS 2006), September 20-24. O-okayama Campus West Bldg, 9, p. 6. Tokyo Institute of Technology, Tokyo (2006)

    Google Scholar 

  35. Kovács, S., Kóczy, L.T.: Interpolative Fuzzy Reasoning in Similarity based System Reconfiguration. In: Proceedings of IEEE SMC 1999, IEEE International Conference on Systems, Man, and Cybernetics, Tokyo, Japan, vol. V, pp. 226–231 (1999)

    Google Scholar 

  36. Kovács, S.: Similarity Based System Reconfiguration by Fuzzy Classification and Hierarchical Interpolate Fuzzy Reasoning. In: Reusch, B. (ed.) Fuzzy Days 1999. LNCS, vol. 1625, pp. 12–19. Springer, Heidelberg (1999)

    Google Scholar 

  37. Kovács, S., Kubota, N., Fujii, K., Kóczy, L.T.: Behaviour based techniques in user adaptive Kansei technology. In: Proceedings of the 6th International Conference on Virtual Systems and Multimedia, VSMM 2000, Ogaki, Gifu, Japan, October 3-6, pp. 362–369 (2000)

    Google Scholar 

  38. Sz. Kovács, D., Vincze, M., Gácsi, Á., Miklósi, P.: Korondi, Ethologically inspired robot behavior implementation. In: 4th International Conference on Human System Interactions (HSI 2011), Yokohama, Japan, May 19-21, pp. 64–69 (2011)

    Google Scholar 

  39. Kovács, S., Vincze, D., Gácsi, M., Miklósi, Á., Korondi, P.: Fuzzy automaton based Human-Robot Interaction. In: IEEE 8th International Symposium on Applied Machine Intelligence and Informatics (SAMI), Herľany, Slovakia, January 28-30, pp. 165–169 (2010)

    Google Scholar 

  40. Vincze, D., Kovács, S., Gácsi, M., Korondi, P., Miklósi, Á., Baranyi, P.: A Novel Appli-cation of the 3D VirCA Environment: Modeling a Standard Ethological Test of Dog-Human Interactions. Acta Polytechnica Hungarica 9(1), 107–120 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Szilveszter Kovács .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Kovács, S. (2014). Practical Aspects of Fuzzy Rule Interpolation. In: Fodor, J., Fullér, R. (eds) Advances in Soft Computing, Intelligent Robotics and Control. Topics in Intelligent Engineering and Informatics, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-05945-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-05945-7_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05944-0

  • Online ISBN: 978-3-319-05945-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics