A Multi-Criteria Three-Way Decision Making Method in a Picture Fuzzy Probabilistic Decision System

Three-way decision is a decision-making method based on human cognitive process, and its basic idea is to divide a universal set into three pair-wise disjoint regions to cognitive information processing. As the complexity of decision-making environment, cognitive information about alternatives given by decision-makers is uncertain and inconsistent. Picture fuzzy point operator (PFPO) is an effective tool to handle this information. In order to obtain more reasonable and effective decision results, this paper proposes three-way decision models and develops a multi-attribute three-way decision method. Then, we use the proposed method to solve a project investment problem. We define new operators on picture fuzzy numbers by a monotonically increasing binary function and a monotonically decreasing unary function. Then, we build three-way decision models based on PFPO and these new operators. Further, we fully consider the relationship between attributes and the classification of alternatives, and present a multi-criteria three-way decision method. In addition, we compare the proposed method with the existing methods by a project investment problem. We show that PFPO can handle inconsistent and changing cognitive information more accurately through an example. In a project investment problem, the decision results obtained by using the proposed method are the same as those obtained by the existing methods, which shows that the method is effective. By the analysis and comparison with these methods, it is proved that the proposed method is very suitable for dealing with multi-attribute decision-making problem with changing picture fuzzy information and consistent with human cognition.

Automated summary

Three-way decision is a decision-making method based on human cognitive process, aiming to handle uncertain and inconsistent information. A multi-attribute three-way decision method is proposed and applied in a project investment problem to obtain more reasonable and effective results, showing the effectiveness of the approach in dealing with multi-attribute decision-making with changing information.