Probabilistic decision making based on rough sets in interval-valued fuzzy information systems

At present, the representative and hot research is three-way decision based on rough set theory. In addition, this topic has been applied in wide variety of specific. In the article, we aim to discuss the rough set method of decision theory in the background of interval-valued fuzzy information systems (IVFIS). First, the main work is to transform the IVFIS into two kinds of approximate spaces by the defined relations, which are fuzzy approximation space and interval-valued fuzzy approximation space, respectively. Simultaneously, fuzzy probability and IVF probability are considered in the whole process. Second, we study two kinds of decision-theoretic rough set methods by combining the Bayesian decision process. Finally, based on the above decision-making models, some illustrative examples about the credit evaluation of enterprises are introduced to deal with the real value and interval-valued data. These results show that the rough set method of decision theory we proposed has wider applications than decision-theoretic rough sets (DTRS).