@misc{Kosiński_Witold_New_2013, author={Kosiński, Witold and Starosta, Bartłomiej}, copyright={Creative Commons Attribution BY 4.0 license}, address={Warszawa}, journal={Książka = Book}, howpublished={online}, year={2013}, publisher={Instytut Badań Systemowych. Polska Akademia Nauk}, publisher={Systems Research Institute. Polish Academy of Sciences}, language={eng}, 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 nodes of the binary tree and they may be evaluated as real numbers too. The forcing mechanism discussed in this paper is used to assign certainty degrees to sentences involving metasets, and to define basic relations like partial membership or partial equality. We thoroughly investigate here the class of metasets with finite deep ranges which are especially suitable for computer representations because of their finite structure. It turns out, that for sentences involving such metasets it is always possible to assign the degrees of certainty that the sentence is either true or false or both at the same time. Moreover, such sentences do not allow for any hesitancy degree what implies no hesitancy in membership and other basic relations. This property does not hold for sentences involving arbitrary metasets, what is illustrated by the examples.}, title={New trends in fuzzy sets, intuitionistic fuzzy sets, generalized nets and related topics. Volume I: Foundations * Metasets, certainty and uncertainty}, type={Text}, URL={http://rcin.org.pl/Content/198420/PDF/KS-2013-06-T1P11.pdf}, }