Dominance-Based Rough Set Model in Hesitant Fuzzy Information Systems

Hesitant fuzzy information systems have been widely applied in decision-making due to their ability to handle uncertain information. In addition, dominance relationships are often taken into account in many practical decision-making problems. Therefore, it is of great significance to conduct research on hesitant fuzzy information systems involved with dominance relations. In this study, we introduce dominance relations in a hesitant fuzzy information system to make it a dominance-based hesitant fuzzy information system, which can provide a solid new idea for comparing hesitant fuzzy elements. Furthermore, a hesitant fuzzy dominance-based rough set model is constructed, and an attribute reduction method is designed to simplify the dominance-based hesitant fuzzy information system. Further, we propose lower and upper approximation discernibility matrices in the dominance-based hesitant fuzzy decision information system to extract decision rules. In addition, two numerical examples are given to demonstrate the effectiveness of the proposed attribute reduction methods.