Constructing Three-Way Decision of Rough Fuzzy Sets from the Perspective of Uncertainties

From the perspective of human cognition, three-way decision (3WD) explores thinking, problem solving, and information processing in three paradigms. Rough fuzzy sets (RFS) are constructed to handle fuzzy concepts by extending the classical rough sets. In three-way decision with rough fuzzy sets (3WDRFS), current works are mainly concerned with calculating the thresholds according to the given risk parameters to make 3WD with minimum cost. However, in real applications, the risk parameters are given in a subjective way based on expert experience. As a result, the risk parameters may be difficult to accurately obtain in 3WDRFS. To solve this problem, uncertainty measure is introduced into 3WDRFS, which provides a new perspective for 3WD theory. First, the fuzziness-based uncertainty for the average-step-fuzzy sets of RFS is analyzed. Then, based on the average-step-fuzzy sets, a 3WDRFS is proposed with the idea of minimizing the uncertainty loss. Furthermore, the sequential three-way decision of RFS (S3WDRFS) with adaptive thresholds from the perspective of fuzziness is presented. The relevant experiments suggest that the objective function designed in the proposed 3WDRFS is effective and reasonable. Moreover, 3WDRFS based on uncertainty loss has better performance than 0.5-approximation model.