Abstract
Metaset is a new concept of set with partial membership relation. It is directed towards computer implementations and applications. The degrees of membership for metasets are expressed as binary sequences and they may be evaluated as real numbers too.
The forcing mechanism discussed in this paper is used to assign certainty values to sentences involving metasets. It turns out, that for a sentence involving finite first order metasets only its certainty value complements the certainty value of its negation. This is not true in general: sentences expressing properties of metasets may have positive uncertainty value. We supply an example of a sentence which is totally uncertain.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Atanassov, K.T.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20, 87–96 (1986)
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)
Jech, T.: Set Theory: The Third Millennium Edition, Revised and Expanded. Springer, Heidelberg (2006)
Kunen, K.: Set Theory, An Introduction to Independence Proofs. Studies in Logic and Foundations of Mathematics, vol. 102. North-Holland Publishing Company, Amsterdam (1980)
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.: 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)
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)
Starosta, B.: Fuzzy Sets as Metasets. In: Proc. of XI International PhD Workshop (OWD 2009), Conference Archives PTETIS, vol. 26, pp. 11–15 (2009)
Starosta, B., Kosiński, 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)
Starosta, B., Kosiński, W.: Metasets, Certainty and Uncertainty. In: Atanassov, K.T., et al. (eds.) Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics. Systems Research Institute, Polish Academy of Sciences, Warsaw (in printing, 2013)
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
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Starosta, B., Kosiński, W. (2013). Metasets, Intuitionistic Fuzzy Sets and Uncertainty. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2013. Lecture Notes in Computer Science(), vol 7894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38658-9_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-38658-9_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38657-2
Online ISBN: 978-3-642-38658-9
eBook Packages: Computer ScienceComputer Science (R0)