Skip to main content

An Approach to Cardinality of First Order Metasets

  • Conference paper
Artificial Intelligence and Soft Computing (ICAISC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8468))

Included in the following conference series:

  • 2184 Accesses

Abstract

Metaset is a new approach to sets with partial membership relation. Metasets are designed to represent and process vague, imprecise data, similarly to fuzzy sets. They enable expressing fractional certainty of membership, equality, and other relations. Even though the general idea stems from and is firmly suited in the classical set theory, it is directed towards efficient computer implementations and applications.

In this paper we introduce the concept of cardinality for metasets and we investigate its basic properties. For simplicity we focus on the subclass of first order metasets however, the discussed ideas remain valid in general. We also present additional results obtained for finite first order metasets which are relevant for computer applications.

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

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. Atanassov, K.T.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cohen, P.: The Independence of the Continuum Hypothesis 1. Proceedings of the National Academy of Sciences of the United States of America 50, 1143–1148 (1963)

    Article  MathSciNet  Google Scholar 

  3. Jech, T.: Set Theory: The Third Millennium Edition, Revised and Expanded. Springer, Heidelberg (2006)

    Google Scholar 

  4. Kunen, K.: Set Theory, An Introduction to Independence Proofs. Studies in Logic and Foundations of Mathematics, vol. 102. North-Holland Publishing Company, Amsterdam (1980)

    MATH  Google Scholar 

  5. Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  6. Starosta, B.: Application of Meta Sets to Character Recognition. In: Rauch, J., RaÅ›, Z.W., Berka, P., Elomaa, T. (eds.) ISMIS 2009. LNCS (LNAI), vol. 5722, pp. 602–611. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Starosta, B.: Metasets: A New Approach to Partial Membership. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS (LNAI), vol. 7267, pp. 325–333. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  8. Starosta, B.: Representing Intuitionistic Fuzzy Sets as Metasets. In: Atanassov, K.T., et al. (eds.) Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics. Foundations, vol. I, pp. 185–208. Systems Research Institute, Polish Academy of Sciences, Warsaw (2010)

    Google Scholar 

  9. Starosta, B., KosiÅ„ski, W.: Meta Sets – Another Approach to Fuzziness. In: Seising, R. (ed.) Views on Fuzzy Sets and Systems. STUDFUZZ, vol. 243, pp. 509–532. Springer, Heidelberg (2009)

    Google Scholar 

  10. Starosta, B., KosiÅ„ski, W.: Metasets, Intuitionistic Fuzzy Sets and Uncertainty. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 388–399. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  11. Starosta, B., Kosiński, W.: Metasets, Certainty and Uncertainty. In: Atanassov, K.T., et al. (eds.) New Trends in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics. Volume I: Foundations, pp. 139–165. Systems Research Institute, Polish Academy of Sciences, Warsaw (2013)

    Google Scholar 

  12. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Starosta, B. (2014). An Approach to Cardinality of First Order Metasets. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2014. Lecture Notes in Computer Science(), vol 8468. Springer, Cham. https://doi.org/10.1007/978-3-319-07176-3_60

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-07176-3_60

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07175-6

  • Online ISBN: 978-3-319-07176-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics