Skip to main content

A Metasemantic Interpretation of Mamdani Systems

  • Chapter
  • First Online:
Enric Trillas: A Passion for Fuzzy Sets

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 322))

  • 849 Accesses

Abstract

The linguistic interpretation of the aggregation of conclusions in a Mamdani System faces the particular difficulty that the aggregated fuzzy sets are not normal, but truncated at a level determined by the degree of satisfaction of the corresponding premises. Taking in account that since the early works of fuzzy control, the numerical meaning of such aggregations of fuzzy sets is considered to be given by the abscissa of their centroids, a working hypothesis is introduced, which including geometrical and linguistic transformations allows a linguistic interpretation in the context of metasemantics, and represents a small further contribution to Computing with Words.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
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

References

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

    Article  MATH  Google Scholar 

  2. Nguyen, H.T., Walker, E.A.: A first course in Fuzzy Logic. CRC Press, Boca Raton FLA (1997)

    MATH  Google Scholar 

  3. Zadeh, L.A.: From computing with numbers to computing with words - from manipulation of measurements to manipulation of perceptions. IEEE Trans. Circ. Syst. 45, 105–119 (1999)

    Article  MathSciNet  Google Scholar 

  4. Moraga, C.: An essay on the interpretability of Mamdani Systems. In: Trillas, E., Bonissone, P., Magdalena, L., Kacprzyk, J. (eds.) Theory and Experimentation. Homage to Ebrahim Mamdani, pp. 61–72. Springer, Heidelberg (2012)

    Google Scholar 

  5. Moraga, C.: A Metasemantics to refine fuzzy if-then rules. In: 34\(^{\rm th}\) IEEE Int. Symp. Multiple-valued Logic, pp. 148–153. IEEE Press, New York (2004)

    Google Scholar 

  6. Trillas, E., Moraga, C., Sobrino, A.: On ‘Family Resemblance’ with fuzzy sets. In: Joint Conference IFSA/Eusflat, pp. 306–311. Eusflat Press, Lisbon (2009)

    Google Scholar 

  7. Wittgenstein, L.: Philosophical Investigations. Basil Blackwell, London (1973)

    Google Scholar 

  8. Zadeh, L.A.: A fuzzy-set-theoretic interpretation of hedges. Memorandum M-335, Electronics Research Laboratory, University of California, Berkeley (1972)

    Google Scholar 

  9. Macvicar-Whelan, P.J.: Fuzzy sets, the concept of height, and the hedge ‘very’. IEEE Trans. Syst. Man, Cybern. SMC-8, 507–511 (1978)

    Google Scholar 

  10. Trillas, E., Moraga, C., Guadarrama, S., Cubillo, S., Castiñeira, E.: Computing with Antonyms. Studies in Fuzziness and Soft Computing 217, 133–153. Springer, Heidelberg (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Claudio Moraga .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Moraga, C. (2015). A Metasemantic Interpretation of Mamdani Systems. In: Magdalena, L., Verdegay, J., Esteva, F. (eds) Enric Trillas: A Passion for Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-16235-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-16235-5_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16234-8

  • Online ISBN: 978-3-319-16235-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics