Skip to main content
SpringerLink
Log in

Multiple-Valued Logic and Artificial Intelligence Fundamentals of Fuzzy Control Revisited

  • Chapter
Artificial Intelligence in Logic Design

Part of the book series: Artificial Intelligence in Logic Design ((SECS,volume 766))

Abstract

This paper reviews one particular area of Artificial Intelligence, which roots may be traced back to Multiple-valued Logic: the area of fuzzy control. After an introduction based on an experimental scenario, basic cases of fuzzy control are presented and formally analyzed. Their capabilities are discussed and their constraints are explained. Finally it is shown that a parameterization of either the fuzzy sets or the connectives used to express the rules governing a fuzzy controller allows the use of new optimization methods to improve the overall performance.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

  • Alsina, C., Trillas, E. & Valverde, L. (1983). On Some Logical Connectives for Fuzzy Set Theory. Journal of Mathematical Analysis and its Applications 93(1): 15–26.

    Article  MathSciNet  MATH  Google Scholar 

  • Assilian, S. & Mamdani, E. H. (1974). Learning Control Algorithms in Real Dynamic Systems. In Proceedings 4th Int. IFAC/IFIP Conference on Digital Computer Application to Process Control. Zürich.

    Google Scholar 

  • Baldwin, J. F. (1985). A Model of Fuzzy Reasoning Through Multi-Valued Logic and Set Theory. International Journal of Man-Machine Studies 11(3): 351–380.

    Article  MathSciNet  Google Scholar 

  • Castro, J. L. (1995). Fuzzy Logic Controllers Are Universal Approximators. IEEE Transactions on System, Man and Cybernetics 25(4): 629–635.

    Article  Google Scholar 

  • Campo, C. del & Trillas, E. (2000). On Mamdani-Larsen s Type Fuzzy Implications. In Proceeding 8th IPMU, Madrid, 712–716.

    Google Scholar 

  • Cross, V. V. & Sudkamp, Th. A. (2002). Similarity and Compatibility in Fuzzy Set Theory. Heidelberg: Physica Verlag.

    MATH  Google Scholar 

  • Driankov, D., Hellendoorn, H. & Reinfrank, M. (1996). An Introduction to Fuzzy Control. Heidelberg: Springer.

    MATH  Google Scholar 

  • Dubois, D. & Prade, H. (1985). A Review of Fuzzy Set Aggregation Connectives. Information Sciences 36: 85–121.

    Article  MathSciNet  MATH  Google Scholar 

  • Dunn, J. M. & Epstein, G. (eds.) (1977). Modern Uses of Multiple-Valued Logic. Boston: D. Reidel.

    MATH  Google Scholar 

  • Gottwald, S. (1993). Fuzzy Sets and Fuzzy Logic. Braunschweig: Vieweg & Sohn.

    Book  MATH  Google Scholar 

  • Guadarrama, S., Trillas, E., Gutierréz, J. & Fernández, F. (2002). A Step Towards Conceptually Improving Takagi-Sugeno’s Approximation. In Proceedings IPMU’2002 3, 1789–1794.

    Google Scholar 

  • Holmblad, L. P. & Østergaard, J. J. (1982). Control of a Cement Kiln by Fuzzy Logic. In Gupta, M. & Sánchez, E. (eds.) Fuzzy Information and Decision Processes, 389–399. New York: North Holland.

    Google Scholar 

  • Klir, G. J. & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall.

    MATH  Google Scholar 

  • Huertas, J. L., Sánchez S., Barriga A. & Baturone I. (1994). A Hardware Implementation of a Fuzzy Controller Using Analog/Digital Techniques. International Journal of Computers and Electrical Engineering 20(5): 409–419.

    Article  Google Scholar 

  • Klement, P., Mesiar R., Pap E. (2000). Triangular Norms. Dordrecht: Kluwer Academic Publisher.

    MATH  Google Scholar 

  • Lee, C. C. (1990). Fuzzy Logic in Control Systems: Fuzzy Logic Controller. Part I and II. IEEE Trans. Systems, Man and Cybernetics 20(2): 404–418 and 20(2): 419–435.

    Article  MathSciNet  MATH  Google Scholar 

  • Lukasiewicz, J. (1923). On 3-valued Logic. Ruch Filozoficzny 5: 169–171.

    Google Scholar 

  • Mamdani, E. H. (1974). Application of Fuzzy Algorithms for Control of a Simple Dynamic Plant. Proceedings IEE 121(12): 1585–1588.

    Google Scholar 

  • Mamdani, E. H. (1976). Advances in the Linguistic Synthesis of Fuzzy Controllers. International Journal Man-Machine Studies 8: 669–678.

    Article  MATH  Google Scholar 

  • Menger, K. (1942). Statistical Metric Spaces. In Proceedings National Academy of Science USA 28.

    Google Scholar 

  • Moraga, C., Pradera, A. & Trillas, E. (2003). Evolutionary Tunning of Fuzzy If-then Rules at the Level of Operations: A Proposal. Actas III Congreso Español sobre Metaheurísticas, Algoritmos evolutivos y bioinspirados MAEB’2003, 530–537. Proceedings 32nd International IEEE Symposium on Multiple-valued Logic. University of Massachusetts at Boston, May 2002. IEEE-CS-Press.

    Google Scholar 

  • Nguyen, H. T. & Walker, E. A. (1999). First Course in Fuzzy Logic. Bocar Raton, FL: CRC Press.

    Google Scholar 

  • Pedrycz, W. (1992). Fuzzy Control and Fuzzy Systems. Research Studies Publisher.

    Google Scholar 

  • Pradera, A., Trillas, E. & Cubillo, S. (2000). On Modus Ponens Generating Functions. International Journal of Uncertainty, Fuzziness and Knowledge Based Systems 8(1): 7–19.

    MathSciNet  MATH  Google Scholar 

  • Rescher, N. (1969). Many-valued Logics. New York: McGraw Hill.

    Google Scholar 

  • Rine, D. (ed.) (1977). Multiple-valued Logic and Computer Science. Amsterdam: North Holland. Second Edition, 1984.

    MATH  Google Scholar 

  • Schweizer, B. & Sklar, A. (1983). Probabilistic Metric Spaces. Amsterdam: North-Holland.

    MATH  Google Scholar 

  • Skala, H. J. (1978). On Many-valued Logics, Fuzzy Sets, Fuzzy Logics and Their Applications. Fuzzy Sets and Systems 1(2): 129–149.

    Article  MathSciNet  MATH  Google Scholar 

  • Skala, H. J., Termini, S. & Trillas, E. (1984). Aspects of Vagueness. Boston: D. Reidel.

    Book  MATH  Google Scholar 

  • Smet, P., Mamdani, A., Dubois, D. & Prade, H. (1988). Non-Standard Logics for Automated Reasoning. New York: Academic Press.

    Google Scholar 

  • Sugeno, M. (1999). Development of an Intelligent Unmanned Helicopter. In Nguyen, H. T. & Prasad, N. R. (eds.) Fuzzy Modeling and Control, 13–43. Boca Raton FL: CRC Press LLC.

    Google Scholar 

  • Sugeno, M. & Murofushi, T. (1991). Helicopter Flight Control Based on Fuzzy Logic. In Proceedings 1st International Fuzzy Engineering Symposium, 1120–1121. Yokohama.

    Google Scholar 

  • Sugeno, M., Guriffin, M. & Bastian, A. (1993). Fuzzy Hierarchical Control of an Unmanned Helicopter. In Proceeding 5th IFSA Congress, 179–182. Seoul.

    Google Scholar 

  • Tanaka, K. (1996). An Introduction to Fuzzy Logic for Practical Applications. New York: Springer-Verlag.

    MATH  Google Scholar 

  • Teodorescu, H. N., Yamakawa, T. & Rascanu, A. (1991). Fuzzy Systems and Artificial Intelligence. Iasi, Romania: Iasi University Publishing House.

    Google Scholar 

  • Trillas, E. (1998). Sobre funciones de negación en la teora de subconjuntos difusos. Stocastica III-1: 47–59 (in Spanish). Reproduced (English version) in Advances of Fuzzy Logic (S. Barro et al. (eds.)), 31–43. Spain: Press of the Universidad de Santiago de Compostela.

    Google Scholar 

  • Trillas, E. & Alsina, C. (2001). On the Joint Verification of Modus Ponens and Modus Tollens in Fuzzy Logic. In Proceedings EUSFLAT’01, 257–260.

    Google Scholar 

  • Trillas, E., Campo, C. del & Cubillo, S. (2000a). When QM-operators Are Implication Functions and Condicional Fuzzy Relations. International Journal of Intelligent Systems 15: 647–655.

    Article  MATH  Google Scholar 

  • Trillas, E., de Soto, A. R. & Cubillo, S. (2000b). A Glance at Implitation and T- Conditional Functions. In Novak, V. & Perfiliera, I. (eds.), Discovering the World with Fuzzy Logic, 126–147. Heidelberg: Physic-Verlag.

    Google Scholar 

  • Trillas, E. & Guadarrama, S. (2001). On Logical Aspects of Numerical Fuzzy Inference. In Proceedings IFSA 2001, 998–1002. IEEE-CS-Press.

    Google Scholar 

  • Trillas, E. & Pradera, A. (2002). Non-functional Fuzzy Connectives: The Case of Negations. In Proceedings ESTYLF 2002, 527–532. Spain: Press of the University of Leon.

    Google Scholar 

  • Trillas, E. & Valverde, L. (1985a). On Implications and Indistinguishability in the Setting of Fuzzy Logic. In Kacprzyk, J. & Yager, R. R. (eds.) Management of Decision Support Systems Using Fuzzy Sets and Possibility Theory, 198–212. Köln: Verlag TUV Rheinland.

    Google Scholar 

  • Trillas, E. & Valverde, L. (1985b). On Mode and Implication in Aproximate Reasoning. In Gupta, M.M. et al. (eds.) Approximate Reasoning in Expert Systems, 157–166. Amsterdam: North Holland.

    Google Scholar 

  • Watanabe, H., Dettloff, W. & Yount, K. E. (1990). A VLSI Fuzzy Logic Controller with Reconfigurable, Cascadable Architecture. IEEE Jr. Solid State Circuits 25(2): 367–382.

    Google Scholar 

  • Whalen, T. & Schott, B. (1985). Alternative Logics for Approximate Reasoning in Expert Systems: A Comparative Study. International Journal of Man-Machine Studies 22(3): 327–346.

    Article  Google Scholar 

  • Yagishita, O., Itoh, O. & Sugeno, M. (1999). Application of Fuzzy Reasoning to the Water Purification Process. In Nguyen, H. T. & Prasad, N. R. (eds.) Fuzzy Modeling and Control, 98–104. Boca Raton, FL: CRC Press LLC.

    Google Scholar 

  • Yamakawa, T. (1988). High Speed Fuzzy Controller Hardware System: The Mega FIPS Machine. Information Sciences 45: 113–128.

    Article  MathSciNet  Google Scholar 

  • Yasunobu, S. et al (1985). Automatic Train Operation System by Predictive Fuzzy Control. In M. Sugeno (ed.) Industrial Applications of Fuzzy Control, 1–18. Amsterdam: Elsevier Science.

    Google Scholar 

  • Zadeh, L. A. (1965). Fuzzy Sets. Information and Control.

    Google Scholar 

  • Zadeh, L. A. (1972). A Rationale for Fuzzy Control. Journal of Dynamic Systems, Measurements and Control 34, 3–4.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Inteligencia Artificial Universidad Politécnica de Madrid, Campus de Montegancedo, 28660, Madrid, Spain

    Claudio Moraga, Enric Trillas & Sergio Guadarrama

Authors
  1. Claudio Moraga
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Enric Trillas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergio Guadarrama
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Moraga, C., Trillas, E., Guadarrama, S. (2004). Multiple-Valued Logic and Artificial Intelligence Fundamentals of Fuzzy Control Revisited. In: Artificial Intelligence in Logic Design. Artificial Intelligence in Logic Design, vol 766. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2075-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-2075-9_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6583-4

  • Online ISBN: 978-1-4020-2075-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation