Metasets, Intuitionistic Fuzzy Sets and Uncertainty

摘要

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.