Metaset is a new concept of set with partial membership relation. Although based on the classical set theory, themetaset theory is directed towards computer implementations and applications due to computer oriented definitions of basic relations and algebraic operations. The degrees to which membership, non-membership and uncertainty relations for metasets are satisfied, are represented by sets of nodes of the binary tree. In this paper we focus on the representation of intuitionistic fuzzy sets by means of metasets. In particular we show how to represent an uncertainty degree by means of two metasets. Also, we define a numerical evaluation of degrees represented by sets of nodes. As the main result we construct a family of metasets that correspond to elements of the given intuitionistic fuzzy set. Their uncertainty, nonmembership and membership degrees to another dedicated metaset, evaluated as real numbers, are equal to the degrees of corresponding elements of the intuitionistic fuzzy set.
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