Three-way decisions of rough vague sets from the perspective of fuzziness

Vague set, as well as intuitionistic fuzzy set, is an extended model of fuzzy sets. On the basis of fuzzy sets, vague sets describe the membership degree of a vague concept by using an interval value instead of a single value. To a certain degree, vague sets have a more powerful ability to process fuzzy information than fuzzy sets. Thus, when characterizing a target concept by vague sets, identifying methods to make scientific and reasonable decisions has become an essential issue. However, existing decision methods always focus on the decisions based on fuzzy concepts, and research on how to make three-way decisions based on vague concepts is still lacking. Therefore, in this paper, the concept of rough vague sets is proposed to construct a rough approximation framework of vague concepts. Then, the fuzziness of the existing approximation approaches is analyzed. Next, improved step-vague set model which is a better approximation approach than existing approaches and the algorithm used to search for a improved step-vague set are proposed. Furthermore, based on the improved step-vague sets, probabilistic rough vague sets and a three-way approximation model with shadowed sets are introduced. Finally, several illustrative examples and relative experiment are listed to verify the effectiveness and significance of the proposed models.