Shandong University of Finance and Economics
Considering the advantage of interval type-2 fuzzy sets (IT2FSs) in describing highly uncertain information, this paper extends IT2FSs to decision-theoretic rough sets (DTRSs), and proposes two novel interval type-2 fuzzy (IT2F) decision-making approaches for deriving three-way decisions. In the IT2F information system without class labels, the interpretation of loss function and the determination of conditional probability are two fundamental issues to be addressed. Based on the properties of IT2FSs, IT2FSs are firstly introduced into DTRSs, which offers a novel illustration for the loss function. Then, in light of Bayesian decision procedure, an IT2F DTRS (IT2FDTRS) model is established. In addition, two methods are designed for deriving three-way decisions with the aid of two IT2F ranking techniques, namely, the combined ranking method and the possibility degree. Meanwhile, IT2F grey relational analysis is used to determine the conditional probability. Furthermore, two three-way decision methods are proposed based on the IT2FDTRS in the IT2F information system. The proposed approaches not only considers the decision risk, but also tells us the ranking results and objective classification results of alternatives, which can replenish the decision results of grey relational analysis. Finally, a practical example is provided to demonstrate the validity of the proposed three-way decision methods.