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.

模糊集的三向逼近作为核心的概括和模糊集的支持，提供了对模糊集的广义定性解释。直觉模糊集 (IFS) 通过联合使用隶属函数和非隶属函数来概括模糊集。在本文中，我们提出了一个模型，用于根据三向决策 (3WD) 的 TAO（三分作用 - 结果）框架构建 IFS 的三向近似。给定一个 IFS，我们使用它的成员和非成员函数作为一对评估来三等分对象的整体，以产生 IFS 的三向近似。我们提出了一个通用的优化模型，用于根据距离函数和三个动作的成本的最小成本原则确定所需参数。