Nothing Special   »   [go: up one dir, main page]

Skip to main content

Random Set-Based Approaches for Modelling Fuzzy Operators

  • Chapter
Modelling with Words

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2873))

Abstract

In this work two approaches for extending set functions to fuzzy set functions are presented. The first approach describes an extension mechanism based on a random set interpretation of fuzzy sets. In the second approach fuzzy sets are interpreted on the basis of random trivalued sets. Examples showing that both techniques exhibit behaviours that are well-suited for modelling different tasks such as fuzzy quantification, fuzzy cardinality and fuzzy temporal operators are presented.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

Similar content being viewed by others

References

  1. Baldwin, J.F., Lawry, J., Martin, T.P.: Mass assignment theory of the probability of fuzzy events. Fuzzy Sets and Systems 83, 353–367 (1996)

    Article  MathSciNet  Google Scholar 

  2. Bordogna, G., Pasi, G.: Modeling vagueness in information retrieval. In: Agosti, M., Crestani, F., Pasi, G. (eds.) ESSIR 2000. LNCS, vol. 1980, pp. 207–241. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Bosc, P., Lietard, L., Pivert, O.: Quantified statements and database fuzzy querying. In: Bosc, P., Kacprzyk, J. (eds.) Fuzziness in Database Management Systems. Studies in Fuzziness, vol. 5, pp. 275–308. Physica-Verlag, Heidelberg (1995)

    Google Scholar 

  4. Cariñena, P., Bugarín, A., Mucientes, M., Díaz-Hermida, F., Barro, S.: Fuzzy Temporal Rules: A Rule-based Approach for Fuzzy Temporal Knowledge Representation and Reasoning. In: Technologies for Constructing Intelligent Systems, vol. 2, pp. 237–250. Springer, Heidelberg (2002)

    Google Scholar 

  5. Delgado, M., Sánchez, D., Vila, M.A.: Fuzzy cardinality based evaluation of quantified sentences. International Journal of Approximate Reasoning 23(1), 23–66 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Díaz-Hermida, F., Bugarín, A., Barro, S.: Definition and classification of semifuzzy quantifiers for the evaluation of fuzzy quantified sentences. Journal of Approximate Reasoning (2003) (in press)

    Google Scholar 

  7. Díaz-Hermida, F., Bugarín, A., Cariñena, P., Barro, S.: Evaluación probabilística de proposiciones cuantificadas borrosas. In: Actas del X Congreso Español Sobre Tecnologías y Lógica Fuzzy (ESTYLF 2000), pp. 477–482 (2000)

    Google Scholar 

  8. Díaz-Hermida, F., Bugarín, A., Cariñena, P., Barro, S.: Un esquema probabilístico para el tratamiento de sentencias cuantificadas sobre fórmulas. In: Actas del XI Congreso Español Sobre Tecnologías y Lógica Fuzzy (ESTYLF 2002), pp. 391–396 (2002)

    Google Scholar 

  9. Díaz-Hermida, F., Bugarín, A., Cariñena, P., Barro, S.: Voting model based evaluation of fuzzy quantified sentences: a general framework. Technical Report GSI-02-01, Intelligent Systems Group. Univ. Santiago de Compostela (2002)

    Google Scholar 

  10. Díaz-Hermida, F., Cariñena, P., Bugarín, A., Barro, S.: Probabilistic evaluation of fuzzy quantified sentences: Independence profile. Mathware and Soft Computing VIII(3), 255–274 (2001)

    Google Scholar 

  11. Dubois, D., Prade, H.: Fuzzy cardinality and the modeling of imprecise quantification. Fuzzy Sets and Systems 16, 199–230 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  12. Dubois, D., Prade, H.: Measuring properties of fuzzy sets: A general technique and its use in fuzzy query evaluation. Fuzzy Sets and Systems 38, 137–152 (1989)

    Article  MathSciNet  Google Scholar 

  13. Glöckner, I.: DFS- an axiomatic approach to fuzzy quantification. TR97-06, Techn. Fakultät, Univ. Bielefeld (1997)

    Google Scholar 

  14. Glöckner, I.: A framework for evaluating approaches to fuzzy quantification. Technical Report TR99-03, Universität Bielefeld (May 1999)

    Google Scholar 

  15. Glöckner, I.: Advances in DFS theory. TR2000-01, Techn. Fakultät, Univ. Bielefeld (2000)

    Google Scholar 

  16. Glöckner, I., Knoll, A.: A formal theory of fuzzy natural language quantification and its role in granular computing. In: Pedrycz, W. (ed.) Granular computing: An emerging paradigm. Studies in Fuzziness and Soft Computing, vol. 70, pp. 215–256. Physica-Verlag, Heidelberg (2001)

    Google Scholar 

  17. Kruse, R., Gebhardt, J., Klawonn, F. (eds.): Foundations of Fuzzy Systems. John Wiley and Sons Inc., Chichester (1994)

    Google Scholar 

  18. Lawry, J.: Possibilistic normalisation and reasoning under partial inconsistency. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9(1), 413–436 (2001)

    MATH  MathSciNet  Google Scholar 

  19. Lee, E.S., Zhu, Q. (eds.): Fuzzy and evidence reasoning. Studies in Fuzziness, vol. 6. Physica-Verlag, Heidelberg (1995)

    MATH  Google Scholar 

  20. Ralescu, A.L.: Cardinality, quantifiers, and the aggregation of fuzzy criteria. Fuzzy Sets and Systems 69, 355–365 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  21. Ralescu, A.L., Ralescu, D.A., Hirota, K.: Evaluation of fuzzy quantified expresssions. In: L. Ralescu, A. (ed.) IJCAI-WS 1997. LNCS, vol. 1566, pp. 234–245. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  22. Sánchez, D.: Adquisición de relaciones entre atributos en bases de datos relacionales. Tesis Doctoral. PhD thesis, Universidad de Granada. E.T. S. de Ingeniería Informática (1999)

    Google Scholar 

  23. Shafer, G. (ed.): A mathematical theory of evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  24. Thomas, S.F.: Fuzziness and Probability. ACG Press (1995)

    Google Scholar 

  25. Wygralak, M.: Fuzzy cardinals based on the generalized equality of fuzzy subsets. Fuzzy Sets and Systems 18, 143–158 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  26. Wygralak, M.: Questions of cardinality of finite fuzzy sets. Fuzzy Sets and Systems 102, 185–210 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  27. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, parts 1-3. Information Sciences 8, 199–279 (1975), 301–357 (1975); 9, 43–80 (1975)

    Article  MathSciNet  Google Scholar 

  28. Zadeh, L.A.: A theory of approximate reasoning. In: Hayes, J.E., Michie, D., Mikulich, L.I. (eds.) Machine Intelligence, vol. 9, pp. 149–194. Wiley, New York (1979)

    Google Scholar 

  29. Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23, 421–427 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  30. Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Comp. and Machs. with Appls. 8, 149–184 (1983)

    Google Scholar 

  31. Zadeh, L.A.: Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems 4(2), 103–111 (1996)

    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

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Díaz-Hermida, F., Cariñena, P., Bugarín, A., Barro, S. (2003). Random Set-Based Approaches for Modelling Fuzzy Operators. In: Lawry, J., Shanahan, J., L. Ralescu, A. (eds) Modelling with Words. Lecture Notes in Computer Science(), vol 2873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39906-3_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-39906-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20487-9

  • Online ISBN: 978-3-540-39906-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics