Semantics of soft sets and three-way decision with soft sets

The theory of three-way decision provides an effective tool for decision-making under uncertainty and incomplete information, when a two-way decision is difficult to make. Soft sets conceptualize and represent special types of uncertainty. In this paper, we suggest two plausible semantics of soft sets for modeling uncertainty, namely, a multi-context semantics and a possible-world semantics. Under the two semantics, we investigate three-way decision under uncertainty represented by soft sets. We introduce a qualitative model of three-way decision based on the core and support of a soft set. We formulate a quantitative model by a) transforming a soft set into a fuzzy set, b) transforming the resulting fuzzy set into a shadowed set (i.e., a three-way approximation of the fuzzy set), and c) making three-way decision with the shadowed set. The results bring additional insights into soft sets, fuzzy sets, interval sets, and shadowed sets for decision making under uncertainty.