Skip to main content

Metasets: A New Approach to Partial Membership

  • Conference paper
Artificial Intelligence and Soft Computing (ICAISC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7267))

Included in the following conference series:

  • 2225 Accesses

Abstract

Metaset is a new concept of set with partial membership relation. It is designed to represent and process vague, imprecise data – similarly to fuzzy sets. Metasets are based on the classical set theory primitive notions. At the same time they are directed towards efficient computer implementations and applications. The degrees of membership for metasets are expressed as finite binary sequences, they form a Boolean algebra and they may be evaluated as real numbers too. Besides partial membership, equality and their negations, metasets allow for expressing a hesitancy degree of membership – similarly to intuitionistic fuzzy sets. The algebraic operations for metasets satisfy axioms of Boolean algebra.

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  MathSciNet  MATH  Google Scholar 

  2. Bolc, L., Borowik, P.: Many-valued Logics 1: Theoretical Foundations. Springer, Heidelberg (1992)

    MATH  Google Scholar 

  3. Goguen, J.: L-fuzzy Sets. Journal of Mathematical Analysis and Applications 18, 145–174 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hwu, W.W.: GPU Computing Gems Emerald Edition. Applications of GPU Computing. Morgan Kaufmann (2011)

    Google Scholar 

  5. Kunen, K.: Set Theory, An Introduction to Independence Proofs. No. 102 in Studies in Logic and Foundations of Mathematics. North-Holland Publishing Company (1980)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Starosta, B.: Character Recognition Java Applet, http://www.pjwstk.edu.pl/~barstar/Research/MSOCR/index.html

  8. Starosta, B.: Partial Membership and Equality for Metasets. Fundamenta Informaticae, in review

    Google Scholar 

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

    Chapter  Google Scholar 

  10. Starosta, B.: Representing Intuitionistic Fuzzy Sets as Metasets. In: Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics. Volume I: Foundations. pp. 185–208 (2010)

    Google Scholar 

  11. Starosta, B.: Character Recognition with Metasets. In: Document Recognition and Understanding, pp. 15–34. INTECH (2011), http://www.intechopen.com/articles/show/title/character-recognition-with-metasets

  12. Starosta, B., Kosiński, W.: Forcing for Computer Representable Metasets, under preparation

    Google Scholar 

  13. Starosta, B., Kosiński, W.: Meta Sets. Another Approach to Fuzziness. In: Views on Fuzzy Sets and Systems from Different Perspectives. Philosophy and Logic, Criticisms and Applications. STUDFUZZ, vol. 243, pp. 509–522. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Starosta, B. (2012). Metasets: A New Approach to Partial Membership. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2012. Lecture Notes in Computer Science(), vol 7267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29347-4_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29347-4_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29346-7

  • Online ISBN: 978-3-642-29347-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics