A model of three-way approximation of intuitionistic fuzzy sets

A three-way approximation of a fuzzy set, as a generalization of the core and the support of the fuzzy set, provides a generalized qualitatively interpretation of a fuzzy set. An intuitionistic fuzzy set (IFS) generalizes a fuzzy set by using jointly a membership function and a nonmembership function. In this paper, we present a model for constructing a three-way approximation of an IFS according to the TAO (trisecting-acting-outcome) framework of three-way decision (3WD). Given an IFS, we use its membership and nonmembership functions as a pair of evaluations to trisect a universe of objects to produce a three-way approximation of the IFS. We present a general optimization model for determining the required parameters according to the principle of the minimum cost with respect to a distance function and costs of three actions. We use Manhattan distance to illustrate the basic ideas of the optimization model.