A three-way decision method with tolerance dominance relations in decision information systems

In recent years, various medical diagnosis problems have been addressed from the perspective of multi-attribute decision making. Among them, the three-way decision theory can provide a novel scheme to solve medical diagnosis issues under the framework of multi-attribute decision making via considering transforming relationships between loss functions and decision matrices. In this paper, we primarily explore a three-way decision method with tolerance dominance relations in ordered decision information systems. In existing three-way decision models, all objects can be divided into two states, we utilize decision attributes to obtain the set of two states in ordered decision information systems. Then, in order to improve the accuracy of patient classifications, the paper simultaneously considers the influence of loss and gain functions for each object, and uses loss and gain functions to obtain net profit functions as new measurement functions. Meanwhile, a class of three-way decisions in terms of multi-attribute decision making rules based on a tolerance dominance relation is established. In light of the proposed three-way decision method, we further construct a multi-attribute decision making method by using tolerance dominance relations and the constructed method is applied to a medical diagnosis issue of Lymphography. Finally, a comparison analysis and an experimental evaluation are performed to illustrate the feasibility and effectiveness of the presented methodology.