The multi-criteria ranking method for criterion-oriented regret three-way decision

Recently, the criterion-oriented three-way decision has garnered widespread attention as it considers the decision-makers' preferences in handling multi-criteria decision-making problems. However, due to the fact that some criterion-oriented three-way decision models do not accurately consider the specific deviation between the object evaluation value and the criterion preference value when calculating the loss function, some of the objects show the weakness of ranking failure. In order to eliminate this weakness, this paper considers this deviation as the decision-maker's regret psychology, combines the regret theory, proposes a new loss function and constructs a new criterion-oriented regret three-way decision model. Firstly, an innovative approach for determining the loss function is introduced, integrating the decision-maker's basic demands with regret theory. Secondly, thresholds are derived by combining the decision-maker's basic demands with two optimization models. Thirdly, the k-means++ clustering algorithm is employed to derive the objects' fuzzy depictions. Then, this paper proposes a practical method for calculating conditional probabilities by combining the concept of closeness with the fuzzy depictions of the objects. Next, a multi-criteria ranking method founded on criterion-oriented regret three-way decision is proposed. Finally, the applicability of the innovative sequencing method is verified by combining parametric and comparative analyses for the computer hardware selection problem. Additionally, in dataset experiments, the proposed method is further validated on datasets containing known ranking results and datasets containing ordered classification.