Skip to main content

Modalities

  • Conference paper
Book cover Eurofuse 2011

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 107))

Abstract

Hedges play an important role in fuzzy theory, although there are relatively few articles on them. Our aim is to provide a theoretical basis not only for hedges, but also for every type of unary operator. One of them is the negation operator, which was presented in an article [14] concerning the DeMorgan class. In our study we will develop unary operators related to other binary operators by demanding that they satisfy certain properties.

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
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Alsina, C., Schweizer, B., Frank, M.J.: Associative functions: triangular norms and copulas. Word Scientific Publishing, Singapore (2006)

    Book  MATH  Google Scholar 

  2. Baldwin, J.F.: A new approach to approximate reasoning using a fuzzy logic. Fuzzy Sets and Systems 2, 309–325 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  3. Banks, W.: Mixing crisp and fuzzy logic in applications. In: WESCON 1994 Idea/microelectronics Conference Record, Anaheim, CA, pp. 94–97 (1994)

    Google Scholar 

  4. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Studies in Fuzziness and Soft Computing, vol. 221. Springer, Heidelberg (2007)

    Google Scholar 

  5. Bergmann, M., Moor, J., Nelson, J.: Logic book. McGraw-Hill, New York (1990)

    Google Scholar 

  6. Bouchon-Meunier, B.: La Logique Floue. Que sais-je? vol. 2702, Paris (1993)

    Google Scholar 

  7. Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators. New Trends and Applications Studies in Fuzziness and Soft Computing, vol. 97 (2002)

    Google Scholar 

  8. Cat Ho, N., Wechler, W.: Hedge algebras: An algebraic approach to structure of sets of linguistic truth values. Fuzzy Sets and Systems 35, 281–293 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cat Ho, N., Wechler, W.: Extended hedge algebras and their application to fuzzy logic. Fuzzy Sets and Systems 52, 259–281 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chatterjee, A., Siarry, P.: A PSO-aided neuro-fuzzy classifier employing linguistic hedge concepts. Expert Systems with Applications 33(4), 1097–1109 (2007)

    Article  Google Scholar 

  11. De Cock, M., Kerre, E.E.: Fuzzy modifiers based on fuzzy relations. Information Sciences 160, 173–199 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Cox, E.: The fuzzy systems handbook: a practitioner’s guide to building, using, and maintaining fuzzy systems. Academic Press Professional, San Diego (1994)

    MATH  Google Scholar 

  13. Dombi, J., Gera, Z.: On aggregative operators. Information Science, under Review Process

    Google Scholar 

  14. Dombi, J.: DeMorgan systems with infinite number of negation. Information Science (appears in 2011)

    Google Scholar 

  15. Dombi, J.: DeMorgan systems with an infinitely many negations in the strict monotone operator case. Information Sciences (accepted 2011)

    Google Scholar 

  16. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. In: Encyclopedia of Mathematics and Its Applications, vol. 127. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  17. Hellendoorn, H.: Reasoning with fuzzy logic. Ph.D. Thesis, T.U. Delft (1990)

    Google Scholar 

  18. Horikawa, S., Furuhashi, T., Uchikawa, Y.: A new type of fuzzy neural network based on a truth space approach for automatic acquisition of fuzzy rules with linguistic hedges. International Journal of Approximate Reasoning 13, 249–268 (1995)

    Article  MATH  Google Scholar 

  19. Huynh, V.N., Ho, T.B., Nakamori, Y.: A parametric representation of linguistic hedges in Zadeh’s fuzzy logic. International Journal of Approximate Reasoning 30, 203–223 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  20. Jang, J.S.R., Sun, C.T., Mizutani, E.: Neuro-fuzzy and soft computing. Prentice Hall, Upper Saddle River (1997)

    Google Scholar 

  21. Kerre, E.E., De Cock, M.: Linguistic modifiers: an overview. In: Chen, G., Ying, M., Cai, K.-Y. (eds.) Fuzzy Logic and Soft Computing, pp. 69–85. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  22. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer, Dordrecht (2000)

    MATH  Google Scholar 

  23. Lakoff, G.: Hedges: A study in meaning criteria and the logic of fuzzy concepts. Journal of Philosophical Logic 2, 458–508 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  24. Di Lascio, L., Gisolfi, A., Loia, V.: A new model for linguistic modifiers. International Journal of Approximate Reasoning 15(1), 25–47 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  25. Liu, B.D., Chen, C.Y., Tsao, J.Y.: Design of adaptive fuzzy logic controller based on linguistic-hedge concepts and genetic algorithms. IEEE Transactions on Systems Man and Cybernetics, Part B 31(1), 32–53 (2001)

    Article  Google Scholar 

  26. Mesiar, R., Kolesrov, A., Calvo, T., Komornkov, M.: A Review of Aggregation Functions. In: Fuzzy Sets and Their Extension: Representation, Aggregation and Models. Studies in Fuzziness and Soft Computing, vol. 220 (2008)

    Google Scholar 

  27. Rubin, S.H.: Computing with words. IEEE Transactions on Systems Man and Cybernetics, Part B 29(4), 518–524 (1999)

    Article  Google Scholar 

  28. Trksen, I.B.: A foundation for CWW: Meta-linguistic axioms. In: IEEE Fuzzy Information, Processing NAFIPS 2004, pp. 395–400 (2004)

    Google Scholar 

  29. Yager, R.R.: Approximate reasoning as a basis for rule-based expert-systems. IEEE Trans. Systems Man Cybernet, SMC 14, 636–643 (1984)

    MathSciNet  MATH  Google Scholar 

  30. Zadeh, L.A.: The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems 8(3), 199–227 (1983)

    MathSciNet  Google Scholar 

  31. Zadeh, L.A.: Quantitative fuzzy semantics. Information Sciences 3, 159–176 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  32. Zadeh, L.A.: A fuzzy-set - theoretic interpretation of linguistic hedges. Journal of Cybernetics 2(3), 4–34 (1972)

    Article  MathSciNet  Google Scholar 

  33. Zadeh, L.A.: Fuzzy logic = computing with words. IEEE Trans. Fuzzy Systems 4, 103–111 (1996)

    Article  Google Scholar 

  34. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, parts 1. Information Sciences 8, 199–249 (1975)

    Article  MathSciNet  Google Scholar 

  35. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, parts 2. Information Sciences 8, 301–357 (1975)

    Article  MathSciNet  Google Scholar 

  36. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, parts 3. Information Sciences 9, 43–80 (1975)

    Article  MathSciNet  Google Scholar 

  37. Zadeh, L.A.: From computing with numbers to computing with words-From manipulation of measurements to manipulation of perceptions. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 45(1), 105–119 (1999)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dombi, J. (2011). Modalities. In: Melo-Pinto, P., Couto, P., Serôdio, C., Fodor, J., De Baets, B. (eds) Eurofuse 2011. Advances in Intelligent and Soft Computing, vol 107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24001-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24001-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24000-3

  • Online ISBN: 978-3-642-24001-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics