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. (C) 2020 Elsevier B.V. All rights reserved.