A regret theory-based three-way decision approach with three strategies

Breast cancer is a malignant tumor that seriously threatens women’s health. Although classic multi-attribute decision-making (MADM) techniques can handle this kind of medical problem, a decision-maker (DM) can only collect sample data under various indicators for result ranking and analysis. The three-way decision (3WD) theory further supplements a classification scheme. In addition, a DM’s own limited rationality and personality traits have a strong impact on decision-making results. By using a dominance-based rough set approach (DRSA), a new 3WD method based on the regret theory (RT) with optimistic, neutral and pessimistic strategies (3WD-RT-OEP) is constructed in a fuzzy environment, so as to prevent diseases in advance and improve the survival rate of patients. First, attribute weights are calculated based on the similarity between the defined attributes of dominance classes, and a new method for calculating conditional probabilities is proposed to enhance the objectivity of the method by the similarity between object dominance classes and decision classes. Second, the score functions of three strategies are proposed by considering regret and rejoicing values in RT, and specific steps and algorithms of the 3WD-RT-OEP method are given as well. Finally, the validity and rationality of the constructed method are proved by experimental analysis with the support of case studies and supplementary data sets.