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With the increasing complexity of the human social environment, it is impossible to describe each object in detail with accurate numbers when solving multiple attribute decision-making (MADM) problems. Compared with the fuzzy set (FS), the intuitionistic fuzzy set (IFS) not only has obvious advantages in allocating ambiguous values to the object to be considered, but also takes into account the degree of membership and non-membership, so it is more suitable for decision makers (DMs) to deal with complex realistic problems. Therefore, it is of great significance to propose a MADM method under an intuitionistic fuzzy environment. Moreover, compared with the traditional 2WD, by putting forward the option of delay, the decision-making risk can be effectively reduced using three-way decision (3WD). In addition, the binary relations between objects in the decision-making process have been continuously generalized, such as equivalence relation which have symmetrical relationship, dominance relation and outranking relation, which are worthy of study. In this paper, we propose 3WD-MADM method based on IF environment and the objective IFS is calculated by using the information table. Then, the hybrid information table is used to solve the supplier selection problem to demonstrate the effectiveness of the proposed method.

Three-Way Multi-Attribute Decision Making Based on Outranking Relations under Intuitionistic Fuzzy Environments