A three-way decision method with pre-order relations

Three-way decision (3WD) theory has been widely used in solving multi-attribute decision-making (MADM) problems, however the calculation method for semantic interpretations of loss functions and conditional probabilities has not been reasonably addressed. Thus, by virtue of existing studies on 3WD and MADM, a novel 3WD method to MADM is explored in the current paper, which is titled the 3W-MADM method. First, a pair of novel pre-order relations are designed by virtue of the classic TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method, and a new scheme for calculating conditional probabilities is further established. Then, the calculation scheme of loss functions and thresholds is put forward via attribute evaluation values and ideal solutions. In particular, several primary steps and the algorithm of the 3W-MADM method are summed up. Finally, the practicality and validity of the proposed method are demonstrated by a realistic case of lymphography from the UCI database. Moreover, the stability and superiority of the presented method are shown by several experimental analyses.