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.
Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.
Oct 15, 2021
Jul 19, 2021