Three-way multi-attribute decision making under incomplete mixed environments using probabilistic similarity

In recent years, many scholars have explored a variety of methods integrating three-way decision (3WD) and multi-attribute decision making (MADM), which enables the classification and priority ranking of alternatives possible and fully reflects the effectiveness and advantages of 3WD in solving MADM problems. However, few of these methods can effectively deal with the MADM problems with incomplete mixed information that are frequently encountered in real-world situations. This study proposes a three-way MADM method for an incomplete mixed information system (IMIS), where the objective determination of conditional probabilities and utility functions in IMIS without decision label is the pivotal issue. To overcome this issue, we define a probabilistic similarity measure for incomplete mixed information. The probabilistic similarity measure is used to replace the distance measure of classical TOPSIS for estimating the conditional probabilities objectively. The probabilistic similarity class is introduced with arithmetic average method to design a conversion mechanism and obtain the objective relative utility functions of incomplete evaluation values. We then construct a novel 3WD model in IMIS and combine it with two customized ranking principles, to solve the incomplete mixed MADM problems from the perspective of classification and ranking in a more thoughtful and interpretable manner. Our study provides a new perspective for the research on MADM in incomplete mixed information environment. Several examples and experimental comparisons verify the effectiveness and stability of the proposed method. The experiments demonstrate that our method can meet more decision-making requirements and is more accurate and rational in some decision-making scenarios than several prior similar methods. © 2022