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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Atanassov, K.T.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20, 87–96 (1986)
Bolc, L., Borowik, P.: Many-valued Logics 1: Theoretical Foundations. Springer, Heidelberg (1992)
Goguen, J.: L-fuzzy Sets. Journal of Mathematical Analysis and Applications 18, 145–174 (1967)
Hwu, W.W.: GPU Computing Gems Emerald Edition. Applications of GPU Computing. Morgan Kaufmann (2011)
Kunen, K.: Set Theory, An Introduction to Independence Proofs. No. 102 in Studies in Logic and Foundations of Mathematics. North-Holland Publishing Company (1980)
Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Starosta, B.: Character Recognition Java Applet, http://www.pjwstk.edu.pl/~barstar/Research/MSOCR/index.html
Starosta, B.: Partial Membership and Equality for Metasets. Fundamenta Informaticae, in review
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)
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)
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
Starosta, B., Kosiński, W.: Forcing for Computer Representable Metasets, under preparation
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)
Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)