A three-way multi-attribute decision-making method with intuitionistic fuzzy preference relationships based on additive consistency

The three-way decision model becomes an effective method to solve the multi-attribute decision problem by considering the semantic relationship between the loss function and the decision matrix. With the increasing number of uncertain data faced in real-world decision-making problems, traditional multi-attribute decision-making methods perform poorly in complex contexts. To solve this problem, a three-way multi-attribute decision-making method with intuitionistic fuzzy preference relationships based on additive consistency is proposed. Firstly, we give the intuitionistic fuzzy preference relationships based on additive consistency. The preference relationships between different decision schemes are obtained, and the preference information in the matrix is used to calculate the conditional probability under the background of the decision-theoretic rough set. Then, considering the correlation between the loss function and the intuitionistic fuzzy number, the relative loss function is used to find the relative loss and decision threshold in the three decision models, and the decision scheme is classified and ranked by decision rules. Finally, the key steps of the proposed method are briefly described, and the algorithm is applied to the classic supplier selection example to prove the feasibility and effectiveness of the proposed model.