Three-way decision method based on triangular norms in incomplete information systems and its applications in medical diagnosis

Three-way decision, as an extension of traditional two-way decision, was proposed by Yao in 2009, which can effectively avoid unnecessary losses caused by incorrect decisions in the decision-making process. Meanwhile, incomplete hybrid information systems represent the database of the relationship between objects and attributes, which refers to a system with multiple data and missing data. In this paper, based on the fact that many existing literatures involving incomplete hybrid information systems did not fully consider the impact of different conditional attributes on decision attributes and lacked effective aggregation methods to integrate weights and distances, we propose a new three-way decision method to deal with incomplete hybrid information systems with the help of triangular norms. First, in incomplete hybrid information systems, we redefine the distance between two objects based on conditional attributes and give the calculation formula of different data attributes in conditional attributes. At the same time, we define a new weight calculation method based on the relationship between conditional attributes and decision attributes. And then, by the distance between different conditional attributes and their corresponding weights, the hybrid distance is obtained using triangular norms. Furthermore, we use the hybrid distance to get the tolerance relation on the target set of an incomplete hybrid information system, thereby, using this tolerance relation, we get a new decision theoretic rough set model and the corresponding decision rules. Finally, by two experiments involving medical diagnosis, we demonstrate that our model has better classification ability, lower misclassification rate, and better stability compared to other corresponding models, thereby confirming that the proposed model provides a new and effective method for handling incomplete hybrid information systems in practical applications.